Question

A project requires a $2,000 investment. The net cash flows are $350 per year for 10 years. The opportunity cost of capital (RA) is 12%. The company intends to finance the project with $1,000 of interest-bearing debt and $1,000 of equity. The interest rate is 8%. The corporate tax rate is equal to 30%. The company must repay the principal in equal annual installments over 5 years. a. Calculate the adjusted net present value (APV). b. Starting with your answer to part a, suppose issue costs are 5% of the gross proceeds of the equity only. Re-compute the APV.

Answer 1

Solution:

Solution to Question Part a.

The adjusted present value is the Net Present Value of the project assuming full equity financing plus the net present value of the debt finance

We will first calculate the Net Present Value assuming full equity financing

Initial investment, I = $2000

Net cash flows, Cn = $350 per year for n = 10 years

Opportunity cost of capital or discount rate, r = 12% = 0.12

The NPV is calculated as follows:

Net present Value (NPV) = Present value of cash flows - Initial Investment

or the Present value of an annuity is also calculated by the formula below:

PV = Cn { [ (1+r)n - 1 ] [r(1+r)n] }

PV = 350 { [ (1+0.12)10 - 1] [0.12(1+0.12)10] }

PV = 350 { [ 1.1210 - 1] [ 0.12 x 1.1210] }

PV = 350 { [3.105848 - 1] [ 0.12 x 3.105848] }

PV = 350 { 2.105848 0.3727}

PV = $1977.59

Thus NPV = $ 1977.59 - $ 2000

NPV = (-) $22.41

Now coming to the effect of debt financing

The amount of debt = $1,000

Interest rate = 8%

Period of repayment = 5 years (5 equal instalments over 5 years)

Corporate tax rate = 30%

We first need to find the cash outflow each year from repayment of the debt and then adjust it for the effect of savings in taxes from interest payments

PV = Cn { [ (1+r)n - 1 ] [r(1+r)n] }

So substituting the values we have

1000 = Cn { [ (1+0.08)5 - 1 ] [0.08(1+0.08)5] }

1000 = Cn { [ (1.08)5 - 1 ] [0.08(1.08)5] }

1000 = Cn { [ 1.469328 - 1 ] [0.08(1.469328)] }

1000 = Cn { [ 0.469328] [0.11755] }

Cn= 1000 { [ 0.469328] [0.11755] }

Cn= 1000 3.9926

Cn= $250.46

The schedule below shows how much interest is paid each year in each instalment

Year	Opening Balance	Interest paid @ 8%	Instalment	Principal paid	Closing balance
Formula -->		Opg bal x 8%		Instalment - Interest	Opg bal - Principal paid
1	1,000.00	(80.00)	(250.46)	(170.46)	829.54
2	829.54	(66.36)	(250.46)	(184.09)	645.45
3	645.45	(51.64)	(250.46)	(198.82)	446.63
4	446.63	(35.73)	(250.46)	(214.73)	231.90
5	231.90	(18.55)	(250.46)	(231.90)	0.00

The present value of the cash outflows after adjustment of the savings from the tax shield provided by interest is calculated below:

Year	Instalment	Interest paid @ 8%	Tax saving @30% on interest	Instalment + Tax saving	PV factor @12%	Product
n					1/(1+r)n	Adjusted instalment x PV factor
1	(250.46)	(80.00)	24.00	(226.46)	0.89286	(202.19)
2	(250.46)	(66.36)	19.91	(230.55)	0.79719	(183.79)
3	(250.46)	(51.64)	15.49	(234.97)	0.71178	(167.24)
4	(250.46)	(35.73)	10.72	(239.74)	0.63552	(152.36)
5	(250.46)	(18.55)	5.57	(244.89)	0.56743	(138.96)
Total	(844.54)

The initial inflow from the loan is $1000 while the PV of the outflows is (-) $ 844.54

Thus net effect of debt financing is (-) $ 844.54 + $1000 = $155.46

Now the adjusted net present value is the sum of the Net present value calculated above and the debt effcet

So APV = (-) $22.41 + $155.46

Thus the adjusted present value is $133.05.

Solution to Question Part b.

If the issue costs are 5% of the gross proceeds of equity

Issue cost = 5% x $1000 = $50

Since this is incurred at point of time 0, these costs itself are at present value

So the Adjusted Present Value is now = $133.05 - $50

Thus the adjusted present value is = $83.05