Question

Case #4  

APV

Consider a project to produce solar water heaters. It requires a $10 million investment and offers a level after-tax cash flow of $1.75 million per year for 10 years. The opportunity cost of capital is 12%, which reflects the project’s business rick.

Suppose the project is financed with $ 5 million of debt and $5 million of equity. The interest rate is 8% and the marginal tax rate is 35%. An equal amount of the debt will be repaid in each year of the project’s life. Calculate APV.

CASE #5

APR vs EAR

Mary Jo plans to invest some money so that she has $8,000 at the end of three years.

	Option A	Option B	Option C	Option D
APR	5.19%	5.11%	5.20%	5.40%
m/per year	365	12	4	1

How much should she invest today given the choices above?

What is her best choice?

What is the EAR for each account? Support your decision in question 2.

Physical therapy equipment purchase

Your firm needs to buy additional physical therapy equipment that costs $20,000. The equipment manufacturer will give you the equipment now if you will pay $6,000 per year for the next four years. If your firm can borrow money at a 9 percent interest rate, should you pay the manufacturer the $20,000 now or accept the four-year annuity offer of $6,000?

Answer 1

Case #4:

Base case NPV = CF0+V^u = -10 million+ sum of $1.75 million for 10 years discounted at 12%

Now inflow of $1.75 million is an annuity and its present value = $1.75 million*PVIFA (12%,10) = 1.75*5.65 = $9.89 million

Thus base case NPV = -10 million+9.89 million = -$0.11 million or -$110,000

APV = Base case NPV+PV (tax shield)

	(Figures in thousands)
Year	Debt outstanding at EOY	Interest = debt o/s at the end of previous year*8%	Tax shield on interest = interest*35%	PV of tax shield using discount rate of 12%
0	5,000.00
1	4,500.00	400.00	140.00	125.00
2	4,000.00	360.00	126.00	100.45
3	3,500.00	320.00	112.00	79.72
4	3,000.00	280.00	98.00	62.28
5	2,500.00	240.00	84.00	47.66
6	2,000.00	200.00	70.00	35.46
7	1,500.00	160.00	56.00	25.33
8	1,000.00	120.00	42.00	16.96
9	500.00	80.00	28.00	10.10
10	0.00	40.00	14.00	4.51
			Total	507.47398

PV of tax shield = 507.47398 (in thousands) or $507,473.98

Thus APV = -110,000+507473.98

= $397,473.98