CH. 5: cash flow discounting
The Great Giant Corp. has a management contract with its newly hired president. The contract requires a lump sum payment of $25,600,000 be paid to the president upon the completion of her first 9 years of service. The company wants to set aside an equal amount of funds each year to cover this anticipated cash outflow. The company can earn 8 percent on these funds. How much must the company set aside each year for this purpose? afv
$2,050,040.55 AFV = $25,600,000 = C × [(1.089 -1) / 0.08]; C = $2,050,040.55
Your car dealer is willing to lease you a new car for $419 a month for 60 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 5.2 percent, what is the current value of the lease? aduepv
$22,191.41 AduePV= 419 * 1-[1/[1+(.052/12)]^60] / .052/12 >>> * 1+ (.052/12)
You are scheduled to receive annual payments of $11,300 for each of the next 21 years. Your discount rate is 10 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year? (AduePV-APV)
$9,773
Todd is able to pay $310 a month for 4 years for a car. If the interest rate is 6.2 percent, how much can Todd afford to borrow to buy a car?
13,148.50
The Good Life Insurance Co. wants to sell you an annuity which will pay you $710 per quarter for 20 years. You want to earn a minimum rate of return of 5.6 percent. What is the most you are willing to pay as a lump sum today to buy this annuity apv
34,038.21 APV= 1-[1/[1=(.056/4)]^20*4]/.056/4
What is the future value of $1,050 a year for 5 years at a 7 percent rate of interest? (AFV)
6,038.28 AFV= $1,050 × [(1.075 - 1) / 0.07]
Your credit card company charges you 1.12 percent per month. What is the annual percentage rate on your account? apr
APR = 1.12 percent × 12 = 13.44 percent
You are considering an annuity which costs $56700 today. The annuity pays $4500 a year. The rate of return is 6 percent. What is the length of the annuity time period? (Do not round intermediate calculations.) APV
APV = $56700 = $4500 × {[1- [1 / (1 + 0.06)t]] / 0.06} 1 / 1.06t = 1- [($56700) (0.06) / 4500] 1 / 1.06t = 1- 0.7560 1 / 1.06t = 0.2440 1.06t = 4.0984 t = ln4.0984 / ln1.06 t = 1.4106 / 0.058268908 = 24.21 years
Your parents are giving you $310 a month for 5 years while you are in college. At a 8 percent discount rate, what are these payments worth to you when you first start college?
APV= $310[1-[1/[1=.08/12]]^5*12/.08/12] $15288.71
You borrow $7,030 to buy a car. The terms of the loan call for monthly payments for 7 years a rate of interest of 8 percent. What is the amount of each payment?
C = $109.57 APV=7030= C * 1-[1/[1=.08/12]]^7*12/.08/12 7,030 = 64.15926 C
You are paying an effective annual rate of 14.60 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on your account? EAR>>r
EAR = 0.146 = [1 + (r/12)]12 - 1 (0.146 + 1)1/12 = 1 + (r / 12) r = (1.1461/12 -1) × 12 r = 13.71 percent
Mr. Miser loans money at an annual rate of 23 percent. Interest is compounded daily. What is the actual rate Mr. Miser is charging on his loans? EAR
EAR = [1 + (0.23 / 365)]365 - 1 = 25.85 percent
One year ago, the Jenkins Family Fun Center deposited $3,600 in an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $5,400 to this account. They plan on making a final deposit of $7,600 to the account next year. How much will be available when they are ready to buy the equipment, assuming they earn a 8 percent rate of return? fv
FV = $3,600 × (1 + 0.08)5 + $5,400 × (1 + 0.08)4 + $7,600 × (1 + 0.08)3 = $22,210.03
Winston Enterprises would like to buy some additional land and build a new factory. The anticipated total cost is $165.21 million. The owner of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire expansion project. Management has decided to save $620,000 a month for this purpose. The firm earns 6 percent compounded monthly on the funds it saves. How long does the company have to wait before expanding its operations? (Do not round intermediate calculations.) (AFV)
Monthly interest rate = 0.06 / 12 = 0.005 AFV = $165,210,000 = $620,000 × {[1.005t - 1} / (0.005)] 2.332 = 1.005t t = ln2.332 / ln1.005 t = 0.847 / 0.005 t = 169.80 months
George Jefferson established a trust fund that provides $166,500 in scholarships each year for worthy students. The trust fund earns a 5 percent rate of return. How much money did Mr. Jefferson contribute to the fund assuming that only the interest income is distributed? pv
PV = $166,500 / 0.05 = $3,330,000
Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $6,600, $11,600, and $17,800 over the next three years, respectively. After that time, they feel the business will be worthless. Marko has determined that a rate of return of 13 percent is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.? (PV)
PV = $6,600 / (1 + 0.13) + $11,600 / (1 + 0.13)2 + $17,800 / (1 + 0.13)3 = $27,261.50
You just paid $354,000 for a policy that will pay you and your heirs $12,600 a year forever. What rate of return are you earning on this policy? r
r = $12,600 / $354,000 = 3.56 percent
