Question

CALCULATE THE FOLLOWING AMOUNTS USING PRESENT VALUE

TABLES.

Shelby Co. bought out the contract of a member of top management for a payment of $80,000 per year for four years at 10% beginning January 1, 20xx.  What is the cost (present value) of the buyout?

         ANSWER = _______________________

What amount must be deposited at the bank today to grow to $6000 in eight years, assuming 12 percent interest compounded quarterly?

         ANSWER = ______________________

Your grandfather would like to share some of his good fortune with you.  He offers to give you money under one of the following scenarios (you get to choose).

$8,000 a year at the end of each of the next eight years.

$50,000 (lump sum) now.

$100,000 (lump sum) eight years from now.

Calculate the present value of each scenario using a 6% interest rate.

Present Value = __________

Present Value = __________

Present Value = __________  

Circle the scenario that maximizes your inheritance.

            

Calculate the present value of each scenario using a 12% interest rate.

Present Value = __________

Present Value = __________

Present Value = __________  

Circle the scenario that maximizes your inheritance.

Answer 1

1. Shelby Co. bought out the contract of a member of top management for a payment of $80,000 per year for four years at 10% beginning January 1, 20xx. What is the cost (present value) of the buyout?

         ANSWER = _278,948_

Workings:

Since the payment starts from the 1^st day, it’s an annuity due. Thus, present value of the buyout is

= {80,000/(1.1)^0} + {{80,000/(1.1)^1} + {{80,000/(1.1)^2} + {{80,000/(1.1)^3}

= 80,000 + 72,727 + 66,116 + 60,105

= 278,948

2. What amount must be deposited at the bank today to grow to $6000 in eight years, assuming 12 percent interest compounded quarterly?

         ANSWER = _2,330_

Workings:

Future Value = 6,000

Time = 8 years

Interest rate; ‘r’ = 12/(100*4) = 0.03

Compounding frequency = quarterly

Therefore, Number of compounding cycle; ‘n’ = 8 * 4 = 32

Present value = Future Value / {(1+r)^n}

= 6,000/ {(1+0.03)^32}

= 6,000 / 2.575

= 2,330

3. Your grandfather would like to share some of his good fortune with you. He offers to give you money under one of the following scenarios (you get to choose).

a) $8,000 a year at the end of each of the next eight years.

b) $50,000 (lump sum) now.

c) $100,000 (lump sum) eight years from now.

Calculate the present value of each scenario using a 6% interest rate.

a) Present Value =_49,680_

b) Present Value = _50,000_

c) Present Value = __62,741_

Circle the scenario that maximizes your inheritance.

Third option maximizes the inheritance.

Workings:

a) $8,000 a year at the end of each of the next eight years.

= 8,000 * {[1-(1+0.06)^(-8) ]/0.06}

= 8,000 * {[1-(0.6274) ]/0.06}

= 8,000 * {0.3726/0.06}

= 8,000 * 6.21

= 49,680

c) $100,000 (lump sum) eight years from now.

Present value = 100,000 / (1.06)^8 = 62,741

           

4. Calculate the present value of each scenario using a 12% interest rate.

a) Present Value = __39,740___

b) Present Value = _50,000___

c) Present Value = __40,388__

In this case second option maximizes the inheritance.

Workings:

a) $8,000 a year at the end of each of the next eight years.

= 8,000 * {[1-(1+0.12)^(-8) ]/0.12}

= 8,000 * {[1-(0.4039) ]/0.12}

= 8,000 * {0.5961/0.12}

= 8,000 * 4.9675

= 39,740

c) $100,000 (lump sum) eight years from now.

Present value = 100,000 / (1.12)^8 = 40,388