Question

Strange corp made the following offer: "Lend us $1mil a year for the next 10 years, we will give you $2 mil a year for the following 10 years (that is, from year 2033 to 2034)

a. if the interest rate for the next 20 years is expected to be 6% per year, should you take this deal?
b. the expected inflation rate is 3% per year over the next 20 years. based on this information, show exactly how your calculation changes and explain why.

Answer 1

a. To determine whether to take the deal, compare the present value of the cash flows. The present value of the $1 million per year for the first 10 years is approximately $7,612,269. The present value of the $2 million per year for the next 10 years is approximately $15,224,538. Therefore, the total present value of the cash flows is approximately $22,836,807. Since the total present value of the cash flows is greater than the amount we need to lend ($10,000,000), we should take the deal. b. The expected inflation rate is 3% per year. To calculate the real interest rate, subtract the inflation rate from the nominal interest rate. The real interest rate is 6% - 3% = 3%. Therefore, the real interest rate for the next 20 years is expected to be 3% per year.

Step-by-step explanation:

a. To determine whether to take the deal, we need to compare the present value of the cash flows. The present value of the $1 million per year for the first 10 years can be calculated using the formula: PV = CF / (1+r)^n

Where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of years. Using this formula, we find that the present value of the $1 million per year is approximately $7,612,269.

Similarly, the present value of the $2 million per year for the next 10 years can be calculated using the same formula. The present value of the $2 million per year is approximately $15,224,538.

Therefore, the total present value of the cash flows is approximately $22,836,807.

To determine whether to take the deal, we compare the present value of the cash flows to the amount we need to lend, which is $10,000,000. Since the total present value of the cash flows ($22,836,807) is greater than the amount we need to lend ($10,000,000), we should take the deal.

b. The expected inflation rate is 3% per year. To calculate the real interest rate, we subtract the inflation rate from the nominal interest rate. The real interest rate is 6% - 3% = 3%. Therefore, the real interest rate for the next 20 years is expected to be 3% per year.