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
Answer:
$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
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
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