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1. Suppose a U.S. treasury bond will pay $2,500 five years from now. If the goin

ID: 2626014 • Letter: 1

Question

1.     Suppose a U.S. treasury bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today?

2.     Five years ago, Greenery Inc. earned $1.50 per share. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period?

3.     You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take your investment to grow to $9,140.20?

4.     You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?

5.     You inherited an oil well that will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the well is 7.5%, how much should you ask for it if you decide to sell it?

6.     Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.

7.     You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%?

Years:       0                      1                      2                      3                      4

                  |                       |                       |                       |                       |

CFs:         $0                 $1,000             $2,000             $2,000             $2,000

8.     You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset?

Explanation / Answer

1.     Suppose a U.S. treasury bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today?

Ans. Bond Worth Today= $2500/(1+0.0425)^5= $2030.30

2.     Five years ago, Greenery Inc. earned $1.50 per share. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period?

Ans. Growth Rate = [(3.2/1.5)^(1/5) - 1] = 0.1636 or 16.36%

3.     You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take your investment to grow to $9,140.20?

Ans. Time(n) = log(9140.2/5000)/log(1.08) = 7.83 ~ 8 years

4.     You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?

Ans. Amt. after 5 years= $3100*[ 1.085^4 + 1.085^3 +1.085^2 +1.085 + 1 ] = $18,368.66

5.     You inherited an oil well that will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the well is 7.5%, how much should you ask for it if you decide to sell it?

Ans. Present Value of all cash flows = $25000 * [1- 1.075^-25] * (1.075/.075) = $299,574.17

6.     Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.

Ans.
Present value of annuity payments = $2,550,000
Rate of return = ?
2,550,000 = 250,000 * (1 - (1+r)^-20) / r
r ~7.7%

7.     You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%?

Years:       0                      1                      2                      3                      4

                  |                       |                       |                       |                       |

CFs:         $0                 $1,000             $2,000             $2,000             $2,000

Ans.
Effective present price = 1000/1.06 + 2000/1.06^2 + 2000/1.06^3 + 2000/1.06^4 = $5986.82

8.     You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset?

Ans.
Rate of return = r =?
7250 = (750/(1+r) +1000/(1+r)^2 + 850/(1+r)^3 + 6250/(1+r)^4)
r ~ 6.5%

9.     Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF%?
Ans.EFF% = [(1+0.18/12)^12 -1] *100 = 19.56%

10.  Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?
Ans. Required Amount = $5000 * ( 1 + 0.0525/360 )^240 = $5178.08

11.  Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?

Ans. Monthly Payments = 130000 / [(1-(1+(0.065/12))^-360)/(0.065/12)] = $821.70

12.  You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?

Ans.
Required months = n
150000 = 3000 * [(1-(1+.07/12)^-n)/(.07/12)]
n ~ 60 months