A large firm received a loan guarantee from the government. Due to the guarantee, the firm can borrow $50 million for five years at 8 percent interest rate per year instead of 10 percent per year. Calculate the value of the guarantee to the firm. (Ignore taxes.)
A)+$53.79 million
B)+$3.79 million
C)−$3.79 million
D)$3.99 million

Question

Quizplus · Accepted Answer

To calculate the value of the guarantee to the firm, we need to find the difference between the interest payments at 8% and 10% over five years on a $50 million loan.

At 8%, the annual interest payment would be:

$50 million x 8% = $4 million

Over five years, this amounts to:

$4 million x 5 = $20 million

At 10%, the annual interest payment would be:

$50 million x 10% = $5 million

Over five years, this amounts to:

$5 million x 5 = $25 million

Therefore, the value of the guarantee to the firm is the difference between the two amounts:

$25 million - $20 million = $5 million

However, this is the total benefit over five years, so we need to calculate the present value of this amount. Assuming a discount rate of 8%, we can use the formula for the present value of an annuity:

PV = C x ((1 - (1 + r)^-n) / r)

where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of periods.

In this case, C is $5 million, r is 8%, and n is 5. Plugging in the numbers, we get:

PV = $5 million x ((1 - (1 + 8%)^-5) / 8%) = $18.21 million

Therefore, the value of the guarantee to the firm is approximately $18.21 million. However, since the question asks for the value of the guarantee relative to the original interest rate of 10%, we need to subtract the present value of the interest payments at 10% over five years, which is:

$5 million x ((1 - (1 + 10%)^-5) / 10%) = $22.00 million

Subtracting this from the value of the guarantee at 8%, we get:

$18.21 million - $22.00 million = -$3.79 million

This means that the value of the guarantee is actually negative, indicating that the firm is worse off with the guarantee than without it. Therefore, the best choice is B, which is the only option that reflects this result.

A Large Firm Received a Loan Guarantee from the Government