Question

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 risk.

a. 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 21%. The debt will be paid off in equal annual installments over the project’s 10-year life. Calculate APV.

b. How does APV change if the firm incurs issue costs of $400,000 to raise the $5 million of required equity?

Answer 1

First of all lets find present value of debt tax shield

Year	Debt	Interest @8%	Tax shield @ 21%	PVIF @ 8%	PV
	A	B = A x 8%	C = B x 21%	D	E = C x D
1	5000000	400000	84000	0.9259	77778
2	4500000	360000	75600	0.8573	64815
3	4000000	320000	67200	0.7938	53346
4	3500000	280000	58800	0.7350	43220
5	3000000	240000	50400	0.6806	34301
6	2500000	200000	42000	0.6302	26467
7	2000000	160000	33600	0.5835	19605
8	1500000	120000	25200	0.5403	13615
9	1000000	80000	16800	0.5002	8404
10	500000	40000	8400	0.4632	3891
					345441

Now let us calculate NPV  

Year	Cash inflow	PVIF @ 12%	PV
1	1750000	0.8929	1562500
2	1750000	0.7972	1395089
3	1750000	0.7118	1245615
4	1750000	0.6355	1112157
5	1750000	0.5674	992997
6	1750000	0.5066	886604
7	1750000	0.4523	791611
8	1750000	0.4039	706796
9	1750000	0.3606	631068
10	1750000	0.3220	563453
PV of cash inflow	9887890
Less : Initial Investment	10000000
NPV	-112110

a) APV = NPV + present value of debt tax shield

=-112110 + 345441

=$2,33,332

b) if the firm incurs issue costs of $400,000 to raise the $5 million of required equity , then APV will change as follows

New APV = 233332 - 400000

=-1,66,668 $