Today is January 1, 2009. The state of Iowa has offered your firm a subsidized loan. It will be in the amount of $10,000,000 at an interest rate of 5 percent and have ANNUAL (amortizing) payments over 3 years. The first payment is due today and your taxes are due January 1 of each year on the previous year's income. The yield to maturity on your firm's existing debt is 8 percent. What is the APV of this subsidized loan? If you rounded in your intermediate steps, the answer may be slightly different from what you got. Choose the closest.

Annual present value of the Payment is $840,797

Given:  

Present value = $10,000,000  029978  

Time = 3 year  

Rate = 5%

Computation:

Payment = Loan / PVAF (3, 5%)

Payment = $3,672,085

Net present value of Cash Flows;  

Cash Flows 0 = $10,000,000  

Cash Flows 1= -$3,502,085

= -$3,172,085 - 0.66 × $500,000  

Cash Flows 2= -$3,556,011  

Cash Flows3= -$3,612,632I = 8%

Annual present value of the Payment = $840,797

Learn more:

link

Complete question:

Today is January 1, 2009. The state of Iowa has offered your firm a subsidized loan. It will be in the amount of $10,000,000 at an interest rate of 5 percent and have ANNUAL (amortizing) payments over 3 years. The first payment is due today and your taxes are due January 1 of each year on the previous year's income. The yield to maturity on your firm's existing debt is 8 percent. What is the APV of this subsidized loan? If you rounded in your intermediate steps, the answer may be slightly different from what you got. Choose the closest.

A. -$3,497,224.43 B. $417,201.05 C.$840,797 D. None of the above

$840,797  is the APV of this subsidized loan

Solution:

Input the loan in a financial equation first and resolve the payment:

PV=10,000,000

N= 3I = 5%

PMT = 3,672,085

Now, find the APV of the loan:

CF0 = $10,000,000

CF1= -$3,502,085

     = -$3,172,085 - .66 * $500,000CF2

     = -$3,556,011CF3

     = -$3,612,632I

     = 8%

APV = $840,797