stock valuation

Ringkasin dikit slide chapter 3 yang di upload di platform oleh Datin Ruhani tentang Stock valuation:


The cash flows of stock ownership come from 1) Dividends and 2) Capital Gains (selling prices greater than purchases price of stock).


Types of stock:
1. Zero growth
2. Constant growth
3. Differential growth




Type 1, Zero growth
Dividends will remain at the same level forever :
D1=D2=D3=….


Since future cash flows are constant, price (value) is the same as present value of a perpetuity:


P0= Div / R




Type 2, Constant growth
Assumes that dividends will growth at the constant rate g forever, i.e. as in growing perpetuity, also called the Dividend Growth Model (DGM):


D1 = D0 (1+g)
D2 = D1 (1+g) = D0 (1+g)2


Thus:
P0 = D1 / R – g




Type 3, Differential growth
Assumes that dividends will grow at different rate in the future and then will grow at the constant rate thereafter.


To find value of the differential growth stock, we need to:
1. Estimate future dividends.
2. Estimate the future stock price when the stock becomes a constant growth stock.
3. Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.


Differential growth example:
Estimate the current value of Karis stock, P0, if its most recent annual dividend payment was RM4 per share and dividends is expected to increase at 8% annual rate for the next 3 years. At the end of third year, the firm is expected to have a slower growth of dividend growth of 5 % per year forever. The firm required return R is 12%.


D1 = D0 (1+g) = RM4 x 1.08 = RM 4.32
PV1 = D1 / (1+R)1 = RM 4.32 / (1+12%)1 = RM3.86
D2 = D1 (1+g) = RM 4.32 x 1.08 = RM 4.67
PV2 = D2 / (1+R)2 = RM 4.67 / (1+12%)2 = RM 3.74
D3 = D2 (1+g) = RM 4.67 x 1.08 = RM 5.04
PV3 = D3 / (1+R)3 = RM 5.04 / (1+12%)3 = RM 3.59


Total PV = RM3.86 + RM 3.74 + RM 3.59 = RM 11.19


Using the constant growth model, the value of stock at the end of the initial growth period is:


D4 = D3 (1+g) = RM5.04 (1.05) = RM 5.292
Thus D4 = RM 5.292, g= 0.05, R = 0.12, using DGM:


P3 = D4/ R – g2 = RM 5.292 / 0.12 – 0.05 = RM75.6
PV = P3 / (1+R)3 = RM 75.6 / (1+12%)3 = RM 54


P0 = RM 11.19 + RM 54 = RM65.19


Estimated for R


R is the required return of the applied discount rate . Return on to a stock depend on:


1. Dividend yield – D/P
2. Growth rate g
P0 = D0 (1+g) / R – g = D1 / R – g
R =( D0 (1+g) / P0) + g = (D1 / P0) + g




Growth Opportunities (NPVGO)
Growth opportunities are opportunities to invest in positive NPV projects.
The value of a firm is the sum of the value of a firm that pays out 100% of its earning (constant earning) as dividends plus the net present value of future expected growth opportunities.


P= (EPS / R) + NPVGO


NPVGO example:


Problem 28,p.157 of text Ross et all 2008:
Information: EPS = CAD 7; investment = - CAD 1.75 per share; earning in yr.1 = CAD 1.90; yr.2 = CAD 2.10; R = 12%.




Value without investment?


P = CAD 7 / 0.12 = CAD 58.33


Value with investment?


NPVGO = C1 /(1+R)1 +C2 / (1+R)2 + C3 / (1+R)3
NPVGO = - CAD 1.75 / (1.12) + CAD 1.90 / (1.12) + CAD 2.10 / (1.12) = CAD 1.62
P = CAD 58.33 + 1.62 = CAD 59.95




Price – Earning Ratio (PE) Ratio
Generally analyst frequently relate earnings per share to prices.


PE ratio reflect the amount investor are willing to pay for each dollar of earning, it thus indicates potential future growth in value of the stock.


The price - earnings ratio is calculated as the current stock price divided by annual EPS. PE multiples however differ between & within industries, thus caution must be used when interpreting potential growth using PE.


P/E ratio = Price per share / EPS

Bond Valuation

Bond Valuation
1. Par (face) value – FV (Future Value), payable at maturity
2. Coupon Rate - %, annual coupon rate / face value
3. Coupon Payment - $, fixed periodic interest payment calculated as : coupon rate x Future Value
4. Maturity Date, determined at issue

Risky Bond Valuation

Bond characteristic
Bond prices and market interest rates move in opposite directions:
1. When C = R, price = par value
2. When C > R, price > par value (premium bond)
3. When C < style="font-weight: bold;">Bond Valuation Formula


Bond Value = c ({1-[1/(1+R)T]} / R ) + (FV/ [1/(1+R)T])


Bond Types:

1. Pure Discount Bonds.
Also known as zeroes, it does not pay periodic coupon payments and sells at discount (less than par value).
Return or yield comes from the difference between the purchase price and the par value.
Valuation of pure discount bond:

PV = FV / /(1+R)T

2. Level Coupon Bonds.
Make periodic coupon payments plus par (face) value at maturity.
Therefore, the bond price (value) is the present value of annuity coupon payment and a terminal (maturity) value.
Coupon payments are normally semiannual.
For bond with semiannual coupon payment, apply = Tx2 and R/2 (ie m = 2).

Valuing bond example:

Find the value of bond if par value = $1000, T=20 years, c = 80% semiannual payment, if:

R = 10%., then T = 20x 2 = 40 and R = 10%/2 = 5%
P = c ({1-[1/(1+R)T]} / R ) + (FV/ [1/(1+R)T])
P = $40 ({1-[1/(1+0.05)40]} / 0.05 ) + ($1000/ [1/(1+0.05)40])
P = $828.41
When R is greater than coupon rate, the bond will sell at discount (less than par).

R = 6%, then R = 6% / 2 = 3% and T = 20 x 2 = 40
P = $40 ({1-[1/(1+0.03)40]} / 0.05 ) + ($1000/ [1/(1+0.03)40])
P = $ 1,231.15
When R is less than coupon rate, the bond will sell at a premium (greater than par).

3. Consols or perpetual bonds
Bonds that does not have maturity period and coupon paid every period till forever. Valuation thus like perpetuity:

PV = c / R

Ashley Wahid Hasyim Jakarta

New Product Development (NPD)

Discuss issues arising from new product development (NPD).

New Product Development

New product development (NPD) is the term used to describe the complete process of bringing a new product service to market. There are two parallel paths involved in the NPD process: one involves the idea generation, product design and detail engineering; the other involves market research and marketing analysis. Definition of new product is new to the world products, new product lines, additional to existing product lines, improvement and revisions on existing products, repositioning and cost reduction. NPD is a process which is designed to develop, test and consider the viability of products which are new to the market in order to ensure the growth or survival of the organization.

Types of new product:
• New to the world products – innovative products, i.e. high tech definition TV, iPod, flat screen TV.
• New product lines – to allow the firm to enter the existing market, i.e. mars ice cream
• Additions to product line – to supplement the firm existing product line, i.e. Weetabix launched Fruitibix
• Improvement or revision of existing products, i.e. new car model
• Repositioned products – existing product targeted at new market
• Cost reductions – new products that provide similar performance at lower cost.

New Product Development:
 Development of a new product
 from idea to launch

The successfully launching a new product, the steps are:
• The idea generation; the idea can be generated from the marketing feedback.
• The idea screening which to screen out the best idea from all the feedback from the customers,
• Chooses the best idea from the pool,
• The firm have to conduct the conceptual development testing,
• The firm have to evaluate the new product if acceptable and material usage and analyze the capability of the firm to proceed with the new product.
• Later market strategy development comes in to determine the target market and the expected market share for the new product.
• From the market strategy development, business analysis is to be done to analyze if the target market and the demand is able to pay of the NPD cost if the business development is appropriate only the new product development
• Firms may produce prototype for market testing purpose and for improvement before actual commercialization.

Example new product is 3D consider New to Malaysian market but once it is "New" to US Market too....it just that this 3D technology takes time to come into Malaysia Market. Further, 3D is also being brought to the TV where nowadays, TV is added with 3D features for better viewing pleasure. Like Universal Studio, 3D is also being built in their games for better experience in the 3D world.

New products are developed for many reasons:

• To add product port folio
• To creates stars and cash cow for the future
• To replace declining products, i.e. new source of energy to replace fuel.
• To take advantage of new technology.
• To maintain/increase market share
• To defeat rivals
• To keep up with rivals
• To maintain competitive advantage
• To fill a gap in the market
• To bring in new customers

To expand the market share, the company would need to face the risk on the new product introduction. that's the reason that the company will not end the existing products when they are introducing a new product, this is part of market strategy in order to test the market on the new products, and at the same time, convey a market survey on the new products, and will have improvement in improving the new products until meet customers' need. However, there are issues arising from NPD, risk in loss on current products, or loss of interest from the customers with this new products, risk of customers in changing to other brands or tastes meaning that when the new products attracted more customers, customers taste will switch to the new products from current products, and as such, sales on current products will reduced or loss.

What about the fact that at least 70% of new products fail in the marketplace? The reasons of failure of launched products:

• Neglect of market research
• Inaccurate market research
• Poor marketing after launch
• Poor distribution
• Product performance below expectation
• Product too complex
• Unforeseen events
• Market not ready for the product
• Inadequate support for the product

Design Thinking:
New Product Development
 Essentials from the Pdma

New products may fail if the idea is favored is pushed through in spite of negative market research findings, maybe the interpretation of the result of survey is incorrect. Over estimated the market size even though the idea is good, firm too optimist on the market size but which in actual demand is not as big as expected. Actual product is not well designed, customer will tend to buy good looking product even though the ugly one is better performance (Sony Erricson beat Nokia before using this technique). Wrongly positioned the product in the market which high end product position in the lower income market, the lower income consumer range are not able to pay for the product. Wrongly priced as if the product is priced too low sometime will raise query that is the product quality is bad. Advertising and promotion strategy not effective as the marketing tool not able to present the meaning they wanted to sell to their target customers and cost of development is higher that project cost which the company not able to recover the expenditure and at the end the company have to operate in loss and the competitor fight back.

Costing of NPD, the high cost usually becomes a put off for companies especially the smaller one. You all mentioned that joint venture with other organizations may help to decrease the cost involved. Why do you need to go all out for NPD when you know that you cannot afford it?

High cost may cause the longer time for Return on Investment (ROI) and for companies that not having a strong cash flow may not able to take such business risk. Joint – Venture (JV) is one of the ways to secure the future business and minimize the business risk. Company need growth to continue survives and every product has the life cycle. To sustain the business, continuously launch of new product is the only way to grow the business.

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Reference:

Tutor2u. (n.d). retrieved from http://tutor2u.net/business/presentations/marketing/newproductdevelopment/default.html.

Forum C, 21/09.2010.

Customers Important?

Elaborate on why you think customers are important in Marketing Management. Give good examples

The Hidden Wealth of Customers:
Realizing the Untapped Value of Your Most Important Asset

• Marketing deals with customers. Marketing is managing profitable customer relationships. The twofold goal of marketing is to attract new customers by promising superior value and to keep and growing current customers by delivering satisfaction (Compiled by Osman Safdar Sarwani from Armstrong & Kotler).

• Customer relationship management (CRM) is the process of communicating with customers throughout the various stages of the purchasing process, and this includes people who have already bought from you. It is significantly easier to hold on to an existing customer than it is to find new ones, but doing this requires all elements of the marketing mix to be run well (product, price, promotion, and placement). From the forum, CRM refers to care, response and management. For example, the response to the customer, customer wanted fast response. Normally, customer will be more satisfy with firm with fast response especially on complaint. In term of care, If a firm care what their customer want and need, they will provide or produce such item to their customer. There are always some unethical business that will produce something that may harm the customers or environment, just because of the profit and the demand in the market. However, it will lies within the firms code of conduct and also the existing local structure and government body to ensure the product available in the market are safe to use. Company has to analyze the feedback and eliminate those unethical one. A firm should welcome all feedback either good or bad, but the companies have to screen through and accept the good one only. For a legal company (Legal company - company that are registered or patent), there are certain certifications or standards that they need to comply to in order to build a certain products. For example, a medical manufacturer will need to comply to the Food and Drugs Association (FDA) certifications. Every firm has to responsible for all of their actions. This is evidence from the government regulations and legislations that are set up to protect the customers. One example is on the melamine milk powder case in China. The few boards of directors of the firm are being sentenced to death by the court of China.The approaches of CRM are:

1. Identify potential prospects and customers (Care),
2. Differentiate customers by needs and value to company (care and response),
3. Interact to improve knowledge and relationship (response),
4. Customize service for each customer (care and management).

The New Successful Large Account Management:
 Maintaining and Growing
Your Most Important Assets -- Your Customers

• Marketing is the process of making customers aware of the products and services of a company. There are two major characteristics of marketing - expanding the existing customer base and the retention of existing customers. Marketing managers need to have a good knowledge of the customer. This means building up an accurate picture using the resources that are available. It is important to take personal opinion out of as many decisions as possible. Information can be gathered from questionnaires, focus groups, the internet, interviews, buying habits and many more sources, but it's important that the information is examined in a scientific way using proper statistical methods. The validity of the survey will depends on how the survey being constructed, (how the questions being asked, direct or indirect) and who is the target of the surveys. Further, the validity of the survey will also depends on the tools and the analysis, i.e. whether a good analysis being done on the results and what kind of analysis tools being used to analyze the results.

• CRM mostly dependent upon technology, customers will also have more confidence with the company with high-technology facilities that will enhance their productivity. CRM also act as a good survey tools to understand own product strength & marketability from time to time and many companies are using CRM for such purpose, especially in FMCG companies, like F&N, Nestle. FMCG industry is more competitive compare to other industry where there is limited product differentiation among the brands, i.e. there is not much product differentiation for instant noodle among Maggie, Cintan, Seddap & Mamee. In this scenario, CRM can an effective tools to retain customer through understand their preference & taste. CRM with the assist of technology help respond to customer needs faster than ever, especially in FMCG who move in the fast pace. High technology products and facilities will be a selling point in promoting a company to the customers. thus, this will be part of CRM, in terms of maintaining or to get new customers.

• Building customers' loyalty is important in maintaining the business and customers. However, there are more than building up customers' loyalty in MM, customer satisfaction, fulfilling customers' requirement, helping customers solving their problem, innovation and creativity are important as well. We need to provide additional services to the customers before our competitive does. Additional service sometimes are not wanted, to determine which one to add and which ones to drop via marketing survey, questionnaires, focus groups, the internet, interviews, buying habits and many more sources. By hiring experts, conducting lots of focus groups, and executing to a detailed plan, the company became deluded that it knew what customers wanted.

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References:
Osmar Safdar Sarwani. (n.d). Retrieved from http://www.scribd.com/doc/5357785/Introduction-to-Marketing-Management
Shivashankar.V.Jirli. (Aug 20th, 2010). Customer Relationship Management: explain the modalities of marketing and customer relations if you are to succeed as a marketing manager firm?. Message posted to http://www.bukisa.com/articles/339608_customer-relationship-management.
Forum B, 21/09/2010

The MBA Decision

Ben Bates graduated from college six years ago with a finance undergraduate degree. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve his goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program.

The Intentional MBA:
 A Guide to Maximizing Your Decision,
Experience and Investment

Ben currently works at the money management firm of Dewey and Louis. His annual salary at the firm is $60,000 per year, and his salary expected to increase at 3 % per year until retirement. He is currently 28 years old and expects to work for 40 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 26 %. Ben has savings account with enough money to cover the entire cost of his MBA program.

The Ritter College of Business at Wilton University is one of the top MBA programs in the country. The MBA degree requires two years of full time enrollment at the university. The annual tuition is $65,000, payable at the beginning of each school year. Books and other supplies are estimated to cost $3000 per year. Ben expects that after graduation from Wilton, he will receive a job offer for about $110,000 per year, with a $20,000 signing bonus. The salary at this job will increase at 4 % per year. Because of the higher salary, his average income tax rate will increase to 31 %.

The Bradley School of Business at Mount Perry College began its MBA program 16 years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one – year program, with a tuition cost of $80,000 to be paid upon matriculation. Books and other supplies for the program are expected to cost $4,500. Ben thinks that he will receive an offer of $92,000 per year upon the graduation, with an $18,000 signing bonus. The salary at this job will increase at 3.5 % per year. His average tax rate at this level of income will be 29 %.
Both schools offer a health insurance plan that will cost $3,000 per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $2,000 more per year at both schools than his current expenses, payable at the beginning of each year. The appropriate discount rate is 6.5 percent.

1. How does Ben’s age affect his decision to get an MBA?
My opinion, Age is one of the important factor that affects someone decision to continue study. In this case, Ben is now 28 years old. He graduated from college six years ago when he’s age is 22 years old. Assuming that Ben already working for about 5 years since graduated from college, so that he would have enough money from salary saving in 5 years to do his MBA at 28 years age. If he starts the MBA program on 28 years old, he will spend two years for study and perhaps finish his MBA at 30 years old. At 30 years old, he will start working again for 40 more years after getting the MBA. With those reasons, age affects his decision for getting an MBA.

2. What other, perhaps no quantifiable factors affect Ben’s decision to get an MBA?
My opinion is there are several non quantifiable factors affect Ben’s decision to get an MBA. First, I think when assuming that Ben already working for about 5 years since graduated from college. he has job experiences as the MBA program usually put the requirement to the candidates at least having two years experiences in his respective field. Second, I think the current family situation. If he married with or without children, this will affect Ben’s decision because spouse or children supporting is also important. The third is his willingness to continue the study. If he eager to continue the study, he will continue the study. But if he has no willingness to study, he could do anything else, for example having jobs that would pay more or open the business.

3.Assuming all salaries are paid at the end of each year, what is the best option for Ben – from a strictly financial standpoint?

I think there are three options have to be calculated:

1.    Keeping his current work for 40 years

There are several factors to be considered to calculate the present values (PV) of the first options are: His annual salary at the firm is $60,000 per year, and his salary expected to increase at 3 % per year until retirement, his current average tax rate is 26 % and discount rate is 6.5 percent.

In this case, to get the present value (PV), we can use the formula of growing annuity.

               

Salary = $60,000, tax rate = 26%, because of tax rate, c = $44,400

                                R (discount rate) = 6.5%

                                G (growth rate) = 3%

                                T (the number of period working) = 40

                                So the PV is = $ 937,474.28

Present Value (PV) of Growing Annuity.

PV_GA =  C (1 – ( (1+g)/(1+r))^t / r – g )

PV_GA= $44 400 (1 – ((1+3%)/(1+6.5%))⁴⁰ / 6.5% - 3%)

PV_GA = $44 400 (1 – ((1.03)/(1.065))⁴⁰ / 0.035)

PV_GA = $ 44 400 (1 – 0.261 / 0.035)

PV_GA = $44 400 (0.739 / 0.035)

PV_GA = $44 400 (21.114)

PV_GA = $ 937,474.28

2.    Getting the MBA at Wilton University

In this case, must compute 4 parts:

A.   PV of salary for 38 years (40 – 2 years)

B.   PV of signing bonus

C.  PV of costs for 2 years (tuition, books and supplies, health insurance and rent fee)

D.  PV of 2 years salary when he would work at the money management firm.

A.   PV of salary for 38 years

The factors to consider are: He will receive a job offer for about $110,000 per year, with a $20,000 signing bonus. The salary at this job will increase at 4 % per year. Because of the higher salary, his average income tax rate will increase to 31 %.

Salary = $110,000, tax rate = 31%, so, C = $75,900

R (discount rate) = 6, 5%

G (growth rate) = 4%

T (the number of period working) = 38 (40 years – 2 years)

So the PV is = $ 1,806,116.4

Present Value (PV) of Growing Annuity.

PV_GA =  C (1 – ( (1+g)/(1+r))^t / r – g )

PV_GA = $75 900 (1 – ( (1+4%)/(1+6.5%))³⁸ / 6.5% - 4%)

PV_GA = $75 900 (1 – ((1.04)/(1.065))³⁸ / 0.025)

PV_GA = $75 900 (1 – (0.9765)³⁸ / 0.025)

PV_GA = $75 900 (1 – (0.40508) / 0.025)

PV_GA= $75 900 (0.5949/0.025)

PV_GA = $75 900 (23.796)

PV_GA = $ 1,806,116.4

B.    PV of signing bonus

The factors to consider are:

Signing bonus = $ 20,000

R (discount rate) = 6, 5%

T (the number of period working) = 38

So the PV is = $17,633.57

PV = FV / (1+r)^t

PV = $20 000 / (1.065)³⁸

PV = $20 000 / 1.1342

PV = $17,633.57

                

C.    PV of cost for years ((tuition, books and supplies, health insurance and rent fee)

The factors to consider are: tuition $65,000, Books and other supplies are estimated to cost $3000 per year. Health insurance plan that will cost $3,000 per year, room and board expenses will cost $2,000.

Cost = $65 000 + $3000 + $3000 + $2000 = $ 73 000

R (discount rate) = 6, 5%

T (the number of period studying) = 2

So the PV is = $ 132,860

Present Value (PV) of Annuity:

PV_A = c ( 1 – (1/(1+r)^t / r )

PV_A  = $73 000 ( 1 – (1/(1.065)² / 6.5%)

PV_A  = $73 000 ( 1 – (1/1.1342 / 0.065)

PV_A = $73 000 (1 – 0.8817 / 0.065)

PV_A = $73 000 (0.1183 / 0.065)

PV_A = $73 000 (1.82)

PV_A  = $ 132,860

D.   PV of 2 years salary when he would work at the money management firm.

The factors to consider are: His annual salary at the firm is $60,000 per year, and his salary expected to increase at 3 % per year until retirement, his current average tax rate is 26 % and discount rate is 6.5 percent.

Salary = $60,000, tax rate = 26%, because of tax rate, c = $44,400

R (discount rate) = 6.5%

G (growth rate) = 3%

T (the number of period working) = 2

So the PV is = $82,076.51

Present Value (PV) of Growing Annuity.

PV_GA =  C (1 – ( (1+g)/(1+r))^t / r – g )

PV_GA = $44 400 (1 – ((1+3%)/(1+6.5%))² / 6.5% - 3%)

PV_GA = $44 400 (1 – ((1.03)/(1.065))² / 0.035)

PV_GA = $44 400 (1 – 0.9353 / 0.035)

PV_GA = $44 400 (0.0647/0.035)

PV_GA = $44 400 (1.8486)

PV_GA = $82,076.51

The Project Manager's MBA:
How to Translate Project Decisions Into Business Success

3.    Getting the MBA at Mount Perry College

In this case, must compute 4 parts:

A.   PV of salary for 39 years (40 – 1 years)

B.    PV of signing bonus

C.    PV of costs for 2 years (tuition, books and supplies, health insurance and rent fee)

D.   PV of 1 years salary when he would work at the money management firm.

A.   PV of salary for 39 years

The factors to consider are: he will receive an offer of $92,000 per year upon the graduation,. The salary at this job will increase at 3.5 % per year. His average tax rate at this level of income will be 29 %.

Salary = $ 92,000, tax rate = 29%, so, C = $ 65,320

R (discount rate) = 6, 5%

G (growth rate) = 3, 5%

T (the number of period working) = 39

So the PV is = $1,463,821.2

Present Value (PV) of Growing Annuity.

PV_GA =  C (1 – ( (1+g)/(1+r))^t / r – g )

PV_GA = $65 320 (1 – ((1+3.5%)/(1+6.5%))³⁹ / 6.5% - 3.5%)

PV_GA = $65 320 (1 – 0.3277/ 0.03)

PV_GA = $65 320 (0.6723/0.03)

PV_GA = $65 320 (22.41)

PV_GA = $1,463,821.2

B.    PV of signing bonus

The factors to consider are:

 Signing bonus = $ 18,000

R (discount rate) = 6, 5%

T (the number of period working) = 39

So the PV is = $ 15,870.22

PV = FV / (1+r)^t

PV = $18 000 / (1.065)³⁹

PV = $18 000 / 1.1342

PV = $15,870.22

               

C.    PV of cost for 1 years ((tuition, books and supplies, health insurance and rent fee)

The factors to consider are: tuition $ 80,000, Books and other supplies for the program are expected to cost $4,500. Health insurance plan that will cost $3,000 per year, room and board expenses will cost $2,000.

Cost = $ 89,500

R (discount rate) = 6, 5%

T (the number of period studying) = 1

So the PV is = $84,033.34

Present Value (PV) of Annuity:

PV_A = c ( 1 – (1/(1+r)^t / r )

PV_A = $89 500 ( 1 – (1/(1+6.5%)¹ / 6.5% )

PV_A = $89 500 (0.06103 / 0.065)

PV_A = $89 500 (0.93892)

PV_A =$84,033.34

D.   PV of 1 year’s salary when he would work at the money management firm.

The factors to consider are: His annual salary at the firm is $60,000 per year, and his salary expected to increase at 3 % per year until retirement, his current average tax rate is 26 % and discount rate is 6.5 percent.

Salary = $60,000, tax rate = 26%, because of tax rate, c = $44,400

R (discount rate) = 6.5%

G (growth rate) = 3%

T (the number of period working) = 1

So the PV is = $41,736

Present Value (PV) of Growing Annuity.

PV_GA =  C (1 – ( (1+g)/(1+r))^t / r – g )

PV_GA = $44 400 (1 – ((1+3%)/(1+6.5%))¹ / 6.5% - 3%)

PV_GA = $44 400 (1 – 0.9671 / 0.035)

PV_GA = $44 400 (0.0329 / 0.035)

PV_GA = $44 400 (0.94)

PV_GA = $41,736

So the best option for Ben Bates is getting the MBA at Wilton University. He will receive more money after finishing the study and get salary and signing bonus with total present value $1 823 749.97. The present value study expenses at Wilton University (tuition, books and supplies, health insurance and rent fee) is $132 860 and the present value study expenses at Mount Perry College (tuition, books and supplies, health insurance and rent fee) is $84 033.34. Since Ben has savings account with enough money to cover the entire cost of his MBA program, it is the best option for him to get the MBA at Wilton University

4.    Ben believes that the appropriate analysis is to calculate the future value of each option. How would you evaluate this statement?

1.    Keeping his current work for 40 years

There are several factors to be considered to calculate the future values (FV) of the first options are: His annual salary at the firm is $60,000 per year, and his salary expected to increase at 3 % per year until retirement, his current average tax rate is 26 %.

In this case, to get the present value (PV), we can use the formula of growing annuity.

Salary = $60,000, tax rate = 26%, because of tax rate, c = $44,400

G (growth rate) = 3%

T (the number of period working) = 40

So the FV is = $11,639,750.53

FV = PV x (1+r)^t

FV = $937 474.28 (1.065)⁴⁰

FV = $937 474.28 (12.416)

FV = $11,639,750.53

2.    Getting the MBA at Wilton University

In this case, must compute 4 parts:

A.   FV of salary for 38 years (40 – 2 years)

B.    FV of signing bonus

C.    FV of costs for 2 years (tuition, books and supplies, health insurance and rent fee)

D.   FV of 2 years salary when he would work at the money management firm.

A.   FV of salary for 38 years

The factors to consider are: He will receive a job offer for about $110,000 per year, with a $20,000 signing bonus. The salary at this job will increase at 4 % per year. Because of the higher salary, his average income tax rate will increase to 31 %.

Salary = $110,000, tax rate = 31%, so, C = $75,900

G (growth rate) = 4%

T (the number of period working) = 38

So the FV is = $19,771,099.95

FV= PV x (1+r)ⁿ

FV = $1 806 116.4 (1.065)³⁸

FV = $1 806 116.4 (10.94674)

FV = $19,771,099.95

B.    FV of signing bonus

The factors to consider are:

 Signing bonus = $ 20,000

G (growth rate) = 0 %

T (the number of period working) = 38

So the FV is = $ 20,000.43

FV = PV (1+r)ⁿ

FV = $17 633.57 (1.065)²

FV = $20,000.43

C.      FV of cost for 2 years college

FV = PV (1+r)ⁿ

FV = $132 860 (1.065)²

FV = $ 150,693.13

D.      FV of 2 years salary when he would work at money management firm

FV = PV (1+r)ⁿ

FV = $82 076.508 (1.065)²

FV = $93,093.23

               

3.    Getting the MBA at Mount Perry College

In this case, must compute 4 parts:

A.      FV of salary for 39 years (40 – 1 years)

B.      FV of signing bonus

C.     FV of costs for 2 years (tuition, books and supplies, health insurance and rent fee)

D.    FV of 1 years salary when he would work at the money management firm.

 A.   FV of salary for 39 years (40 – 1 years)

The factors to consider are: he will receive an offer of $92,000 per year upon the graduation,. The salary at this job will increase at 3.5 % per year. His average tax rate at this level of income will be 29 %.

Salary = $ 92,000, tax rate = 29%, so, C = $ 65,320

G (growth rate) = 3, 5%

R = 6.5%

T (the number of period working) = 39

So the FV is = $17,065,646.13

FV = PV (1+r)ⁿ

FV = $1 463 821.2 (1.065)³⁹

FV = $17 065 646.13

B.    FV of signing bonus

The factors to consider are:

 Signing bonus = $ 18,000

G (Growth rate) = 0%

T (the number of period working) = 39

So the FV is = $ 18,000.40

FV = PV (1+r)ⁿ

FV = $15 870.22 (1.065)²

FV = $ 18,000.40

C. FV of costs for 2 years (tuition, books and supplies, health insurance and rent fee)

FV = PV (1+r)ⁿ

FV = $84 033.34 (1.065)

FV = $ 89,495.50

D. FV of 1 years salary when he would work at the money management firm.

FV = PV (1+r)ⁿ

FV = $44 400 (1.065)¹

FV = $47,286

By calculate the future value of each option: The present value of his salary $937,474.28 is equal to future value $11,639,750.53 when keeping his current work for 40 years. The present value of salary     $1,806,116.4 is equal to future value $ 19,771,099.95 plus $ 20,000 signing bonus when having a job for 38 years after getting the MBA at Wilton University. The present value of salary $1,463,821.2 is equal to future value $17,065,646.13 plus $18,000 signing bonus when having a job for 39 years after getting the MBA at Mount Perry College. The best choice is he having study at Wilton University.

5.    What initial salary would Ben need to receive to make him indifferent between attending Wilton University and staying in his current position?

Staying in his current position, PV 1 = $937,474.28

Getting the MBA at Wilton University, PV2 = $ 1,804,927.68

When PV1=PV2

21,06C1 = $75,900 * 23,78

21, 06 C1 = $ 1 806 116.4

C1 = $85,760.51

The amount $ 85,760.51 already deducted with 26% taxed, the salary before tax deduction is $ 108,508.2. So, the initial salary would Ben need to receive to make him indifferent between attending Wilton University and Staying in his current position is $108,508.2

6. Suppose, instead of being able to pay cash for his MBA, Ben must borrow the money. The current borrowing rate is 5.4%. How would this affect his decision?
There are two options:

1. Getting the MBA from Wilton University

Ben Bates must borrow $146,000 to get the MBA at the Wilton University for two years. The current borrowing rate is 5, 4%. Assuming he pay out the principal plus interest every year for five years:

Loan amount : $146,000
Interest rate : 5, 4%
Long term : 5
Loan payment : $ 34.096,06

Amortization table 1.0:

	beginning balance	total payment	interest paid	principal paid	ending balance
1	146.000,00	34.096,06	7.884,00	26.212,06	119.787,94
2	119.787,94	34.096,06	6.468,55	27.627,51	92.160,43
3	92.160,43	34.096,06	4.976,66	29.119,40	63.041,04
4	63.041,04	34.096,06	3.404,22	30.691,84	32.349,19
5	32.349,19	34.096,06	1.746,86	32.349,20	(0,01)
	Totals	170.480,30	24.480,28	146.000,01

The total payment in five years is $170.580,30. Then, when we calculated the present value with discount rate 6,5% and period five years:
C = $170.580,30
R (discount rate) = 6, 5%
T (the number of period) = 5
So the PV is = $ 708,875.80

2. Getting the MBA from Mount Perry College

Ben Bates must borrow $ 89,500 to get the MBA at the Mount Perry College for one year. The current borrowing rate is 5, 4%. Assuming he pay out the principal plus interest every year for five years:
Loan amount : $89,500
Interest rate : 5, 4%
Long term : 5
Loan payment : $ 20.901,35
Amortization table 1.1:

	beginning balance	total payment	interest paid	principal paid	ending balance
1	89.500,00	20.901,35	4.833,00	16.068,35	73.431,65
2	73.431,65	20.901,35	3.965,31	16.936,04	56.495,61
3	56.495,61	20.901,35	3.050,76	17.850,59	38.645,02
4	38.645,02	20.901,35	2.086,83	18.814,52	19.830,50
5	19.830,50	20.901,35	1.070,85	19.830,50	0,00
	Totals	104.506,75	15.006,75	89.500,00

The total payment in five years is $104.506,75. Then, when we calculated the present value with discount rate 6,5% and period five years:
C = $104.504,75
R (discount rate) = 6, 5%
T (the number of period) = 5
So the PV is = $ 434,293.44

From the table 1.0, the total payment is 170.480,30 is equal with present value $ 708,875.80. From table 1.1, the total payment is 104.506,75 is equal with present value $ 434,293.44. These will affect his decision to continue study. From strictly financial standpoint, if Ben must borrow the money with current rate 5,4%, he is still can continue the study at Wilton University. Another alternative is that if he is not continue the study, Ben need to receive an initial salary around $107.961,78 to make him indifferent between attending Wilton University and staying in his current position.

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Source:case study "The MBA Decision" from chapter 4, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.

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