A large firm is receiving a loan guarantee from the government. Because of the guarantee, the firm is able to borrow $50 million for five years at 8% interest rate per year instead of
10% 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) None of the above

Question

Quizplus · Accepted Answer

To calculate the value of the guarantee, we need to find the difference between the interest payments made at the 8% rate and the payments that would have been made at the 10% rate.

At 8% per year, the firm will pay: 
8% x $50 million = $4 million per year

At 10% per year, the firm would have paid: 
10% x $50 million = $5 million per year

The difference between these two payments is: 
$5 million - $4 million = $1 million per year

Over a five-year period, the value of the guarantee is: 
$1 million x 5 years = $5 million

Therefore, the value of the guarantee to the firm is positive and equal to $5 million. However, the question asks for the answer in terms of the present value of this stream of payments, which is less than $5 million due to the time value of money. Using a financial calculator, the present value of the five-year stream of payments at a discount rate of 8% is approximately $1.21 million.

The question gives four answer choices that are all different from $5 million, so we need to calculate the present value of the stream of payments to determine which is the closest answer choice.

PV = PMT x [1 - (1 + r)-n] / r 
PV = $1 million x [1 - (1 + 0.08)-5] / 0.08 
PV = $3.79 million

The closest answer choice to this value is B, +$3.79 million. Therefore, the answer is B) +$3.79 million.

A Large Firm Is Receiving a Loan Guarantee from the Government