Deck 3: Opportunity Cost of Capital and Capital Budgeting

Question 1

Identifying the Opportunity Cost of Capital
Don Phelps recently started a dry cleaning business.He would like to expand the business and have a coin-operated laundry also.The expansion of the building and the washing and drying machines will cost $100,000.The bank will lend the business $100,000 at 12 percent interest rate.Don could get a 10 percent interest rate loan if he uses his personal house as collateral.The lower interest rate reflects the increased security of the loan to the bank,because the bank could take Don's home if he doesn't pay back the loan.Don currently can put money in the bank and receive 6 percent interest.
Required:
Provide arguments for using 12 percent,10 percent,and 6 percent as the opportunity cost of capital for evaluating the investment.

Answer 1

Solution to Identifying the Opportunity Cost of Capital (15 minutes)
The 12 percent rate that the bank wants to charge without the security of the home mortgage probably best reflects the risk of the project.Therefore,the 12 percent interest rate is probably the most appropriate discount rate to use.
The 10 percent rate reflects the interest rate that Don Phelps would have to pay if he uses his personal house as collateral.This rate reflects the interest rate for Don's total portfolio of assets including his house.
The 6 percent rate reflects the interest rate that Don receives in interest for his bank deposits.If Don decided to use his own cash and not borrow money for the investment,Don's forgone opportunity of using the cash would be the 6 percent interest if no other investment were available.

Question 2

Financing Charges and Net Present Value
The president of the company is not convinced that the interest expense should be excluded from the calculation of the net present value.He points out that,"Interest is a cash flow.You are supposed to discount cash flows.We borrowed money to completely finance this project.Why not discount interest expenditures?" The president is so convinced that he asks you,the controller,to calculate the net present value including the interest expense.
How can you adjust the net present value analysis to compensate for the inclusion of the interest expense?

Answer 2

Solution to Financing Charges and Net Present Value (15 minutes)
There are probably many possible ways of examining this problem.From a theoretical perspective,of course,interest expense (like dividends)is excluded because it is captured in the discount rate.
But here is another way of viewing an investment.An investment that is entirely debt-financed is a positive NPV project if,at the end of the project,there is excess cash after paying the interest and the principal of the debt.This can be seen in the following equation where early cash flows are re-invested at a rate "r" to pay off the principal of the loan at the end of n periods,which is also the length of the project.
(CF₁)(1+r)^n-1 + (CF₂)(1+r)^n-2 + ....+ (CF_n)> or < Investment (= Principal)
where CF_i = Cash flows in period i including interest payments.
If the left hand side of the equation is greater than the right hand side of the equation,the investment has a positive NPV and is acceptable.This analysis assumes complete debt financing to capture all of the opportunity cost of using cash.

Question 3

Annuity
Suppose the opportunity cost of capital is 10 percent and you have just won a $1 million lottery that entitles you to $100,000 at the end of each of the next ten years.
Required:
a.What is the minimum lump sum cash payment you would be willing to take now in lieu of the ten-year annuity?
b.What is the minimum lump sum you would be willing to accept at the end of the ten years in lieu of the annuity?
c.Suppose three years have passed and you have just received the third payment and you have seven left when the lottery promoters approach you with an offer to "settle-up for cash." What is the minimum you would accept (the end of year three)?
d.How would your answer to part (a)change if the first payment came immediately (at t = 0)and the remaining payments were at the beginning instead of at the end of each year?

Answer 3

Solution to Annuity (15 minutes)
a.The minimum lump sum you should take is the present value of the cash payments. b.This question is essentially (a)in reverse.You are looking for the future value of the cash payments.Looking in the future value in arrears table,the annuity factor is 15.937. c.This is similar to (a).This time,t = 7. d.To convert an end-of-year payment schedule to a beginning-of-year schedule,we need only multiply by 1 + r.The minimum payment is $614,500 × 1.10 = $675,900.

Question 4

Asset Replacement
The Baltic Company is considering the purchase of a new machine tool to replace an obsolete one.The machine being used for the operation has a tax book value of $80,000,with an annual depreciation expense of $8,000.It has a salvage value (resale value)of $40,000,is in good working order,and will last,physically,for at least 10 more years.The proposed machine will perform the operation so much more efficiently that Baltic engineers estimate that labor,material,and other direct costs of the operation will be reduced $60,000 a year if it is installed.The proposed machine costs $240,000 delivered and installed,and its economic life is estimated at 10 years,with zero salvage value.The company expects to earn 14 percent on its investment after taxes (14 percent is the firm's cost of capital).The tax rate is 40 percent,and the firm uses straight-line depreciation.Any gain or loss on the machine is subject to tax at 40 percent.
Should Baltic buy the new machine?