# Time Value of Money

1. B.J. Industries has a current ratio of 2.5, with $2.5 million in current assets. Due to sales growth, the company wants to expand accounts receivable and inventories by taking on additional short-term debt. If B.J. Industries wants to maintain a minimum current ratio of 2.0, what is the maximum additional short-term funding it can borrow?

a.$750,000

c. $150,000

b. $350,000

d. $500,000

2. You are comparing two investment options. The cost to invest in either option is the same today. Both options provide you with $20,000 of income. Option A pays five annual payments of $4,000 each. Option B pays five annual payments starting with $8,000 the first year followed by four annual payments of $3,000 each. Which one of the following statements is correct given these two investment options?

a. Both options are of equal value given that they both provide $20,000 of income.

b. Option A has a higher present value than option B given any positive rate of return.

c. Option B has a higher present value than option A given any positive rate of return.

d. Option B has a lower future value at year 5 than option A given a zero rate of return.

3. Mr. Moore will be 35 years at the end of the month and he wishes to retire in 25 years. He plans to invest in a mutual fund earning 7.5 percent annual return compounded monthly and have a $1.5 million retirement fund at age 60. How much must be deposited at the end of each month to achieve his goal?

a. $2,850 c. $1,449

b. $8,514 d. $1,710

4. You are the manager of an annuity settlement company. Jim Patton just won the state lottery which promises to pay him $1,000 per year for 20 years, starting from today, and $2,000 per year for years 21-45, given a 9% discount rate. Your company wants to purchase the proceeds from the lottery from Jim. What is the most that your company can offer?

a. $13,770.90

b. $18,680.95

c. $23,721.01

d. $12,633.85

5. Jean Cleveland currently has $5,750 in a money market account paying 5.65 percent compounded semi-annually. She plans to use this amount and her savings over the next 5 years to make a down payment on a townhouse. She estimates that he will need $15,000 in 5 years. How much should she invest in the money market account semi-annually over the next 5 years to achieve this target?

a. $ 886.28

b. $ 757.25

c. $ 650.97

d. $ 610.79

6. You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum amount of $50,000 today, or receive payments of $641 a month for 10 years. You can earn 6.5% on your money. Which option should you take and why?

a. You should accept the payments, because they are worth $56,452 today.

b. You should accept the payments, because they are worth $56,737 today.

c. You should accept the $50,000 because the payments are worth only $47,758 today.

d. You should accept the $50,000 because the payments are worth only $47,808 today.

#### Solution Preview

See Excel attachment for better clarity of formulas.

1.

Current liabilities=Current assets/current ratio=2.5/2.5=1 million

Let it borrow x million.

New level of assets=2.5+x

New level of liabilities=1+x

New current ratio=(2.5+x)/(1+x)

Put New current ratio=

(2.5+x)/(1+x)=2

2.5+x=2+2x

x=0.5 million=500,000

2. Let us assume any positive rate of return, r=8%

Year End Cash Flow Cash Flow PV of option A PV of option B

n CFA CFB CFA/(1+r)^n CFB/(1+r)^n

1 4000 8000 3703.70 7407.41

2 4000 3000 3429.36 2572.02

3 4000 3000 3175.33 2381.50

4 4000 3000 2940.12 2205.09

5 4000 3000 2722.33 2041.75

Total ...

#### Solution Summary

There are six problems related to current ratio and time value of money concepts. Solutions are provided in MS Excel format.