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Chapter 15: Problem 2

You are offered the choice of two payment streams: (a) \(\$ 150\) paid one year from now and \(\$ 150\) paid two years from now; (b) \(\$ 130\) paid one year from now and \(\$ 160\) paid two years from now. Which payment stream would you prefer if the interest rate is 5 percent? If it is 15 percent?

Short Answer

Expert verified
At an interest rate of 5%, the results are : \(PV_a\) = \(\$ 285.71\), \(PV_b\) = \(\$ 277.23\). At this rate one would prefer payment stream (a). At an interest rate of 15%, the results are: \(PV_a = \$ 239.82\), \(PV_b = \$ 245.62\). At this rate one would prefer payment stream (b).

Step by step solution

01

Understanding the Payment Streams and Interest Rates

We have two different payment streams (a) and (b) and two different interest rates (5% and 15%). We need to calculate the present value of both payment streams for both interest rates.
02

Calculating Present Values for the first Payment Stream

For payment stream (a), it consists of \(\$ 150\) paid one and two years from now. Thus, the present values using the formula \(PV = FV/(1 + r)^n\) will be: \(PV_a(i) = 150/(1 + i)^1 + 150/(1 + i)^2\). We should calculate this present value for both interest rates 5% and 15%.
03

Calculating Present Values for the second Payment Stream

For payment stream (b), it consists of \(\$ 130\) paid one year from now and \(\$ 160\) paid two years from now. Thus, the present values are: \(PV_b (i) = 130/(1 + i)^1 + 160/(1 + i)^2\). This present value should also be calculated for both interest rates 5% and 15%.
04

Compare Payment Streams

Now we have the present values of both streams for both interest rates, we can simply compare them to decide which payment stream is favored under each interest rate.

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Most popular questions from this chapter

A consumer faces the following decision: She can buy a computer for \(\$ 1000\) and \(\$ 10\) per month for Internet access for three years, or she can receive a \(\$ 400\) rebate on the computer (so that its cost is \(\$ 600\) ) but agree to pay \(\$ 25\) per month for three years for Internet access. For simplification, assume that the consumer pays the access fees yearly (i.e., \(\$ 10\) per month \(=\$ 120\) per year). a. What should the consumer do if the interest rate is 3 percent? b. What if the interest rate is 17 percent? c. At what interest rate will the consumer be indifferent between the two options?

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A bond has two years to mature. It makes a coupon payment of \(\$ 100\) after one year and both a coupon payment of \(\$ 100\) and a principal repayment of \(\$ 1000\) after two years. The bond is selling for \(\$ 966 .\) What is its effective yield?

Suppose the interest rate is 10 percent. If \(\$ 100\) is invested at this rate today, how much will it be worth after one year? After two years? After five years? What is the value today of \(\$ 100\) paid one year from now? Paid two years from now? Paid five years from now?
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