a. Consider the time line below that shows periodic cash flows and interest rates per period. Interest rate/year
0 1 2 3 4 5 6 7 8 9 Time 2,500 -4,000 6,000 -3,700 Cash flows
i. What is the value of the cash flows at T0?
ii. What is the value of the cash flows at T6?
iii. What is the value of the cash flows at T9?
iv. Would you rather receive the cash flows described above, or $700 today? Explain your choice.
b. i. You wish to borrow $100,000 for one year and have had the following offers from two different financial institutions. Which one would you choose?
1. Bank A: 9.0% pa compounded quarterly
2. Bank B: 8.5% pa compounded monthly
ii. If Bank B charged you an upfront fee of 1% of the loan, would this change your decision?
You have decided to set up an education fund so that you will be able to give a needy scholar $1,000 a year, starting in four years' time. To finance the fund you will deposit three equal annual deposits starting today. If the required rate of return is 7.5%, what will be the size of the deposits? 5.6% 4.3% 7.9%
You wish to buy a house for $750,000 and the bank has agreed to give you a 15 year loan for 80% of the purchase price, at an annual interest rate of 9%, compounded monthly. The loan will pay off the interest and capital such that there is no debt outstanding at the end of the loan.
a. What are your monthly repayments, the first being due at the end of the first month?
b. You believe that immediately after the 24th payment, interest rates will rise to 12% pa.
i. If you decide to pay out the loan at that time to avoid the higher interest rate charges, what will be the payout amount?
ii. If you are unable to afford to pay out the loan at that time, how much longer will it take to pay out the loan if you do not adjust the monthly payments?
SSSG Ltd. has just issued a dividend of $1.25 per share on their ordinary shares that have a face value of $1.00. Dividends have been increasing at a rate of 4%pa and this trend is expected to continue for another year. After that the growth rate is expected to be 6%pa for three years before settling down into the long term growth rate of 5%pa. If the market requires a return of 12%pa on these shares:
i. What is their current price?
ii. What is the expected price five years from now?
Three years ago, SSSG Ltd. issued 10 year $1,000 bonds with a 7% coupon rate paid semi-annually, at par value. The market currently requires a 9% yield.
i. What was the price of the bond at issue?
ii. What is the current price of the bond?
iii. If the market yield falls to 6% in two years time, what will the bond's price be at that time?
iv. Explain your results in (i) - (iii)
This case is intended to be an introduction to the various methods used in capital budgeting and looks at some of the decisions that may have to be made when evaluating projects. It is also designed to develop skills in using spreadsheets. You should set up a spreadsheet at the start to help analyse the problems. When using a spreadsheet, any tables that you wish to present to the reader should be embedded into a Word document as an ordinary table.
Although he was hired as a financial analyst after completing his business degree, David Ong's first assignment at Wang Systems was with the firm's marketing department. Historically, the major focus of David's sales effort was on demonstrating the technological superiority of the firm's product line.
However, many of Wang's traditional customers have embarked on cost-cutting programs in recent years, and as a result, Wang's marketing director asked David's boss, the Chief Financial Officer, to lend David to marketing to help them develop some analytical procedures for the sales force to use that will demonstrate the financial benefits of buying Wang's products.
Wang Systems manufactures fluid control systems that are used in a wide variety of applications, including sewage treatment systems, petroleum refining, and pipeline transmission. The complete systems include sophisticated pumps, sensors, and control units that continuously monitor the flow rate and the pressure along a line, and automatically adjust the pump to meet preset pressure specifications. Most of Wang's systems are made up of standard components, and most complete systems are priced from $50,000 to $100,000. Because of the highly technical nature of the products, the majority of Wang's sales force have backgrounds in engineering.
As he began to think about his assignment, David quickly came to the conclusion that the best way to 'sell' a system to a cost-conscious customer would be to conduct a capital budgeting analysis which would demonstrate the system's cost effectiveness. Further, he concluded that the best way to begin was with an analysis for one of Wang's actual customers.
From discussions with the firm's sales people, David decided that a proposed sale to Selangor River Council (SRC) was perfect to use as an illustration. SRC is considering the purchase of one of Wang's standard fluid control systems which costs $80,000 including taxes and delivery. It would cost SRC another $5,000 to install the equipment, and this expense would be added to the invoice price of the equipment to determine the depreciable basis of the system. For taxation purposes the system can be depreciated over 6 years, using the following schedule, but has an economic life of 8 years and it will be used for that period. After 8 years, the system will probably be obsolete, so it will have a zero salvage value at that time. Current depreciation allowances are:
Year 1: 20% Year 2: 32% Year 3: 19%
Year 4: 12% Year 5: 11% Year 6: 6%
This system would replace a control system which has been used for about 20 years and which has been fully depreciated. The costs for removing the current system are about equal to its scrap value, so its current net market value is zero.
The advantages of the new system are that (i) it would be more energy efficient, (ii) it would reduce waste, because the chemical processes could be more carefully controlled, and (iii) it would require less human monitoring and maintenance. In total, the new system would save SRC $25,000 annually in before-tax operating costs. For capital budgeting, SRC uses a 10% cost of capital, and the applicable tax rate is 40%.
Mary Seong, Wang's marketing manager, gave David a free hand in structuring the analysis. Now put yourself in David's position and develop a capital budgeting analysis for the fluid control systems. As you go through the analysis, keep in mind that the purpose of the analysis is to help Wang's sales representatives sell equipment to other nonfinancial people, so the analysis must be as clear as possible, yet technically correct. In other words, the analysis must not only be right, it must also be understandable to decision makers, and the presenter - David, in this case - must be able to answer all questions, ranging from the performance characteristics of the equipment to the assumptions underlying the capital budgeting decision criteria.
What is the project's net present value (NPV)? Explain the economic rationale behind the NPV. Could the NPV of this particular project be different for SRC than for one of Wang's other potential customers? Explain.
Calculate the proposed project's internal rate of return (IRR). Explain the rationale for using the IRR to evaluate capital investment projects. Could the IRR for this project be different for SRC than for another customer? Explain.
Suppose one of SRC executives uses the payback method as a primary capital budgeting decision tool and wants some payback information.
a. What is the project's payback period?
b. What is the rationale behind the use of payback period as a project evaluation tool?
c. What deficiencies does payback have as a capital budgeting decision method?
d. Does payback provide any useful information regarding capital budgeting decisions?
SRC have a fixed overhead cost of $1.5 million per annum. How should this be allocated to the present system for project evaluation?
What would the cash flows be in Yr 0 if the existing control system had -
a. A book value of $7,000 and a salvage value of $5,000
b. A book value of $7,000 and a salvage value of $10,000.
A third capital budgeting decision that David is able to make is when to abandon a system. Consider a system that has an engineering life of 4 years (that is, the system will be totally worn out after 4 years).
However, if the system were taken out of service, or 'abandoned' prior to the end of 4 years, it would have a positive salvage value. Here are the estimated net cash flows for the system.
Year Initial Investment and
Operating Cash Flow
Abandonment Cash Flow
0 ($50,000) $50,000
1 24,000 30,000
2 18,000 20,000
3 12,000 5,000
4 5,000 0
The relevant cost of capital is again 10%. What would the NPV be if the system was operated for the full 4 years? What if it was abandoned at the end of Year 3? Year 2? Year 1? What is the economic life of the system?