Time value of money

Your family members know you are taking this class and you learned about time value of money. Four of them came separately to ask questions relating to time value of money. Use the applicable interest table at the end of the book to compute the unknowns for your four relatives. Note that each is independent.

a.Your cousin asked how much he must contribute at the end of the each of the next eight years if he wants to accumulate $90,000 in his account by the end of the eighth year. Cousin told you the interest is compounded annually and the account will earn interest rate of 8%.

b.Your 40-year old Aunt plans to retire at age 65. She is getting a late start but wants to start contributing towards her retirement from now (age 40) through age 64. How much must she contribute each year if he plans to accumulate $500,000 by the time he retires; if he will earn 12% annual interest and interest is compounded annually?

c.Your sister owes $47,347 on her student loan. She wants to pay off before she retires. She has $20,000 today and she will invest the $20,000 in an account that pays 9% interest. How many years will it take for the $20,000 to grow so she can have enough money to pay off the $47,347 debt assume the debt amount is fixed?

d.Your uncle currently has a $27,600 loan. He plans to repay the loan in four years. She plans to invest $19,553 for the next four years and use the principal and interest balance in the account to pay off the loan. What rate of interest must your uncle earn annually so he can have enough to pay off the loan?

2.DT International (DT) intends to purchase equipment. To get the best price, DT asked for bids from vendors. Analysis shows that each equipment from the vendors is similar and has estimated useful life of 20 years.

Additionally, each equipment will have year-end maintenance costs as follows:

Year 1-5 Year 6-15 Year 16-20

Cost per year $1,000 $2,000 $3,000

Below are the packages of three vendors:

Vendor 1: DT pays $55,000 cash at time of delivery and payments of $18,000 at end of each of the next 10 years. DT can elect to purchase a 20-year maintenance service agreement for $10,000 one-time fee. The purchase agreement is optional but if purchased, DT won’t have to maintain the equipment for a fee for the useful life of the equipment. (Use PV of ordinary annuity table)

Vendor 2: Sales price is $380,000. Payment of $9,500 is payable semi-annually for 20 years. Upon delivery, DT pays $9,500. Then, it makes remaining 39 payments starting 6 months after delivery. The annual maintenance for the next 20 years is included in the price. (Use PV of annuity due table; remember the payment is twice a year, so interest rate will be half of annual interest rate provided below).

Vendor 3: Sales price is $150,000. DT must pay the whole sales price at delivery. (Use PV of ordinary annuity table but take into consideration the years of the maintenance cost).

Required

Assume DT will pay for the maintenance contract with vendor 1 if selected and that vendor 2

will perform maintenance at no extra charge as indicated. Since Vendor 3 doesn’t offer maintenance, DT will pay for this based on the year-end maintenance cost provided. Which vendor should DT select if its cost of funds is 10%? (Hint: calculate which one has the lowest PV of cash outflows).

 

3.A small business owner (Craig Osborn) has a defined-benefit retirement plan for him and three employees. At retirement, Craig will get 50% of his last-year before retirement’s annual salary while each employee will get 40% of his or her last-year before retirement’s annual salary. The company will fund the plan by making 15 annual contributions. The plan’s compound annual interest rate is 12%. The plan will make annual payment to each participant at the beginning of each year for 20 years starting from retirement date.

 

She provides you the following salary and retirement information current as of January 1, 2015 (This is the date the 15 annual contributions to the plan starts).

 

Name Current Annual Salary Estimated Retirement Date

Craig Osborn $48,000 January 1, 2040

Dean Smith $36,000 January 1, 2045

Danny Aubrey $18,000 January 1, 2035

Pamela Langford $15,000 January 1, 2030

Each year-end, Craig and his employees will have raises of 4%.

Required

a. What is the annual retirement benefit for each plan participant? (Round to the nearest dollar.) Hint: Craig will receive raises for 24 years, Dean will receive raises for 29 years, Danny will receive raises for 19 years, and Pamela will receive raises for 14 years.

b. What amount must be contributed to the plan at the end of 15 years to ensure that all benefits will be paid? (Round to the nearest dollar.) Hint: calculate the PV of annuity for each participant then total. Note that Craig will retire 10 years after contributions stop, Dean will retire 15 years after contributions stop, Danny will retire 5 years after contributions stop, and Pamela will retire the beginning of the year after contributions stop.

c. What is the required annual beginning of the year contributions? Recall that annual compounded interest rate is 12%.

 

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