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. Here, the payment is being made at the beginning of each year, so we have to calculate the Present Value of annuity due of payments.

Cost (Present value) of the buyout = Present value of annuity due of 4 years at 10% * $80000

= 3.48685 * $80000 = $278950

2. Here Iinterest is compunded quarterly, so while calculating present value, we will take interest as 12% /4 =3%, and time will be 8*4 = 32 years

Since there will be a single payment that will grow to $6000 in 8 years, so we will calculate simple present value

Present value = $6000 / (1+.03)³²

= $6000 / (1.03)³²

= $6000 / 2.575

=$2330

3. Using 6% interest rate.

a) Here payment is made at the end of each year, so will calculate present value of annuity.

Present value of $8000 a year at the end of each year, for next 8 years = Present value of annuity for $8000

= 6.2098 * $8000 = $49678

b) Lump sum now = $50000 , which is present value now.

c) Here payment will be made after 8 years, so we will calculate simple present value.

Present value of $100000 at the end of 8 years = 0.627 * $100000

= $62700

We can see that present value is maximum ($62700), if we take lump sum of $100000, eight years from now. So, it will maximise the inheritence.

Using 12% interest rate.

a) Here payment is made at the end of each year, so we will calculate present value of annuity.

Present value of $8000 a year at the end of each year, for next 8 years at 12% = Present value of annuity for $8000

= 4.9676 * $8000 = $39740

b) Lump sum now = $50000 , which is present value now.

c) Here payment will be made after 8 years, so we will calculate simple present value.

Present value of $100000 at the end of 8 years at 12% = 0.404 * $100000

= $40400

We can see that present value is maximum ($50000), if we take lump sum of $50000 now. So, it will maximise the inheritence.