MBA 800 – Homework #3Time Value of Money and Interest Rates

Dr. Stanley D. Longhofer

1) Walt is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $12,500; year 2, $10,000; year 3, $7,500; year 4, $5,000; year 5, $2,500; year 6, $0; and year 7, $12,500. Walt believes that he should earn an annual rate of 9 percent on this investment. How much should he pay for this investment?

Year Return Rate – 9%

1 12500

2 10000 NPV(r,CF0, L1,L2)

3 7500 PV = $ 37,680.95

4 5000

5 2500

6 0

7 12500

2) Consider an investment that will pay $680 per month for the next 15 years and will be worth $28,000 at the end of that time. How much is this investment worth to you today at a 5.25 percent discount rate?

FV = $28000

I = 5.25% PV = $98,266.75 using calculator

N = 15 years

PMT = 680

P/Y = 12

3) Suppose you deposit $5,000 into an account earning 4 percent interest, compounded monthly.

a) How many years will it take for your account to be worth $7,500?

PV = $5000 N = ?

FV = $7500 N = 121.8434 months

I = 4%

Compounded Monthly

b) Suppose in addition to the initial $5,000 deposit, you will make monthly contributions of $50. How many years will it take for the account to grow to $7,500 in this case?

PMT = 50, PpY = 12 Therefore, N = 35.394 Months

4) Consider an investment that will pay you $2,000 per month for each of the next 2 years, and then $5,000 per month in the following 3 years.

a) If your required rate of return on this investment is 18 percent per year, what is the most you would be willing to pay for it?

NOTE: Your cash flow worksheet does NOT incorporate the P/Y setting. Thus, you must use periodic interest rates when calculating the NPV with irregular cash flows.

$2000 / month for 2 years

$5000/ month for 3 years PV = 10,490.60

I = 18 % I/month = 18/12 = 1.5%

b) Suppose you can purchase this investment for $150,000. What is its net present value? Should you purchase this investment?

NPV = PV – Cost = 10490.6 – 150000 = - 139509.4 NO PURCHASE

5) The yield on 1-year Treasury securities is 6%, 2-year securities yield 6.2%, and 3-year securities yield 6.3%. There is no maturity risk premium. Using the pure expectations theory, forecast the yields on the following securities:

a) A 1-year Treasury security, 1 year from now.

(1+r1)=1.06, Therefore r1 = 6%

b) A 2-year Treasury security, 1 year from now.

6%

6) Explain briefly what it means when we say that we have an “inverted yield curve.” What does this imply about investor’s expectations regarding future interest rates?

Inverted yield curve is when the long term interest rate is lower than the short term interest rate. Therefore, investors would expect future interest rates to drop and hence they would prefer to borrow on a short-term basis and then re-borrow when the rates have dropped. Inverted yield curve is considered as a sign of slow economy.

7) Problem 5-27 from the text: Can the nominal interest rate available to an investor be significantly negative? (Hint: consider the interest rate earned from saving cash “under the mattress.”) Can the real interest rate be negative? Explain.

Nominal Interest rates are the rates quoted by banks or financial institution. These rates cannot be negative because even if you just put money under a mattress, you will earn 0%.

Real interest rate is basically the nominal interest rate less the rate of inflation. This can be negative if the rate of inflation is higher than the nominal interest rate.

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