Question

Suppose that a risk-free investment will make three future payments of $100 in one year, $100 in two years, and $100 in three years.

Instructions: Round your answers to 2 decimal places.
a. If the Federal Reserve has set the risk-free interest rate at 16 percent, what is the proper current price of this investment?
b. What is the price of this investment if the Federal Reserve raises the risk-free interest rate to 18 percent?

Answer 1

The current price of the risk-free investment with a risk-free interest rate of 16 percent is $224.46. If the interest rate is increased to 18 percent, the price would be $211.32.

Step-by-step explanation:

To calculate the current price of the risk-free investment, we need to discount the future payments to their present values using the interest rate. Let's start with part a:

a. The proper current price of the investment can be calculated using the present value formula:

Price = Payment / (1 + Interest Rate)^n

Where Payment is the future payment, Interest Rate is the risk-free interest rate, and n is the number of years until the payment. Plugging in the values, we get:

Price = $100 / (1 + 0.16)^1 + $100 / (1 + 0.16)^2 + $100 / (1 + 0.16)^3

= $86.21 + $74.23 + $64.02 = $224.46

Therefore, the proper current price of this investment is $224.46.

b. If the Federal Reserve raises the risk-free interest rate to 18 percent, we just need to substitute the new interest rate into the formula:

Price = $100 / (1 + 0.18)^1 + $100 / (1 + 0.18)^2 + $100 / (1 + 0.18)^3

= $84.75 + $69.60 + $56.96 = $211.32

Therefore, the price of this investment would be $211.32 if the Federal Reserve raises the risk-free interest rate to 18 percent.

Answer 2

The proper current price of the investment with a 16% risk-free interest rate is $224.60. If the Federal Reserve raises the risk-free interest rate to 18%, the price of the investment would then be $217.51.

To calculate the current price of an investment based on future payments, we can use the present value formula. This takes into account the time value of money, which acknowledges that money available at the present time is worth more than the same amount in the future due to its potential earning capacity.

For the risk-free investment with 16% interest rate:

The present value (PV) of each payment can be calculated as follows:

• PV Year 1 = $100 / (1 + 0.16)1
• PV Year 2 = $100 / (1 + 0.16)2
• PV Year 3 = $100 / (1 + 0.16)3

Total PV = PV Year 1 + PV Year 2 + PV Year 3
Total PV = $86.21 + $74.32 + $64.07
Total PV = $224.60

For the risk-free investment with 18% interest rate:

Following the same method for an increased interest rate:

• PV Year 1 = $100 / (1 + 0.18)1
• PV Year 2 = $100 / (1 + 0.18)2
• PV Year 3 = $100 / (1 + 0.18)3

Total PV = $84.75 + $71.86 + $60.90
Total PV = $217.51