Question

Problem 18-12 APV MVP, Inc., has produced rodeo supplies for over 20 years. The company currently has a debt-equity ratio of 65 percent and the tax rate is 21 percent. The required return on the firm's levered equity is 14 percent. The company is planning to expand its production capacity. The equipment to be purchased is expected to generate the following unlevered cash flows: Year Cash Flow 0 $18,900,000 WN- 5,820,000 9,620,000 8,920,000 The company has arranged a debt issue of $9.66 million to partially finance the expansion. Under the loan, the company would pay interest of 10 percent at the end of each year on the outstanding balance at the beginning of the year. The company also would make year-end principal payments of $3,220,000 per year, completely retiring the issue by the end of the third year. Calculate the APV of the project. (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89) APV

Answer 1

Adjusted present value (APV) =NPV of the cash flows of a project +NPV of the benefits of financing (both discounted at unlevered cost of equity)

So, first, we need to find the unlevered cost of equity

for that , we use the formula,

Rs=Ro+(B/S)*(1-Tc)*(Ro-Rb)

where,we have the explanations & values for the above, as follows:

Rs=Levered Cost of equity= 14%

Ro=Unlevered cost of equity---- to be found out??

Rb=Cost of debt= 10%

B/S=0.65

Tc=Tax rate= 21%

Now, plugging the above values, in the formula,

we can find the cost of unlevered equity as,

0.14=Ro+0.65*(1-0.21)*(Ro-0.1)

Solving for Ro,

Cost of unlevered equity=12.64%

Now we will use this 12.64% to discount to discount the given cash flows for the project

So, the NPV of the cash flows=

-18900000+(5820000/1.1264^1)+(9620000/1.1264^2)+(8920000/1.12^3)=

198088.12

Now, we need to add the NPV of the interest tax shields

so, we can find the interest payment for the three years ,using the foll. Amortisation table

	Payment towards			ITS
Year	Inerest	Principal	Princ. Bal.	Int.*Tc 30%
0			9660000
1	966000	3220000	6440000	289800
2	644000	3220000	3220000	193200
3	322000	3220000	0	96600

Discounting the annual tax expense saved at the Unlevered cost of equity capital, ie. 12.64%

NPV of ITS=(289800/1.1264^1)+(193200/1.1264^2)+(96600/1.1264^3)=

477145.06

so, the APV of the project=NPV of the cash flows+NPV of the tax benefots of Debt

ie. 198088.12+477145.06=

675233.18

Answer:
APV=	675233.18

Discounting the annual tax expense saved at the cost of debt, ie. 10%

NPV of ITS=(289800/1.1^1)+(193200/1.1^2)+(96600/1.1^3)=

495700.98

Now, the APV will be

ie. 198088.12+495700.98=

693789.10