Question

You need to choose cases that you want to solve. Find the cases that worth 70 points in total (mix between 10, 20 and 30 points). You cannot choose more than 70 points.

Case no. 1 (10 points) Congratulations! You have just won the lottery! However, the lottery bureau has just informed you that you can take your winnings in one of two ways. Choice X pays $1,000,000. Choice Y pays $1,750,000 at the end of five years from now. Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.)

Case no. 2 (10 points)

$100 is received at the beginning of year 1, $200 is received at the beginning of year 2, and $300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is

Case no. 3 (20 points)

To expand its operation, the International Tools Inc. (ITI) has applied for a $3,500,000 loan from the International Bank. According to ITI's financial manager, the company can only afford a maximum yearly loan payment of $1,000,000. The bank has offered ITI, 1) a 3-year loan with a 10 percent interest rate, 2) a 4-year loan with a 11 percent interest rate, or 3) a 5-year loan with a 12 percent interest rate.

(E) Compute the loan payment under each option.

(b) Which option should the company choose?

Case no. 4 (30 points)

Mr. & Mrs. Pribel wish to purchase a boat in 8 years when they retire. They are planning to purchase the boat using proceeds from the sale of their property which is currently worth $90,000 and its value is growing at 7 percent a year. The boat is currently worth $200,000 increasing at 5 percent per year. In addition to the value of their property, how much additional money should they deposit at the end of each year in an account paying 9 percent annual interest in order to be able to buy the boat upon retirement?

Answer 1

CASE 1 -

PV of X = 1,000,000

PV of Y = 1,750,000/(1.05)^5 = 1371170.791

Therefore, we would choose Y as we are getting more in the present terms!

FV of X = 1,000,000(1.05)^5 = 1,276,281.563
FV of Y = 1,750,000

Therefore, we would choose Y as we are getting more in the future terms!

This shows that it doesn't matter which approach we choose.

CASE 2 -

The future value of the cash flow is = 100(1.12)^3 + 200(1.12)^2 + 300(1.12) = 727.3728

 

CASE 3 -

PART A.

Loan Payment for first one –

FV = 3500000(1.1)^3 = 4658500

Loan Payment => x/(1.1) + x/(1.1)^2 + x/(1.1)^3 = 4658500
Therefore x = 1407401

Loan Payment for second one –

FV = 3500000(1.11)^4 = 5313246.40

Loan Payment => x/(1.1) + x/(1.1)^2 + x/(1.1)^3 + x/(1.1)^4 = 5313246.40
Therefore x = 1128142

Loan Payment for third one –

FV = 3500000(1.12)^5 = 6168195.89

Loan Payment => x/(1.1) + x/(1.1)^2 + x/(1.1)^3 + x/(1.1)^4 = 6168195.89
Therefore x = 970934

PART B.

The company should choose 3rd option as it can only afford maximum loan payment of 1,000,000. So we have loan payment in third option = 970934 which is less than 1,000,000.

 

CASE 4 -

FV of property after 8 years @7% is 90000(1.07)^8 = 154636.75

FV of boat after 8 years @5% is 200000(1.05)^8= 295491.08

Total amount still required = 295491.08-154636.75 = 140854.33

Therefore this amount is required at the end of each year is

x/(1.09) + x/(1.09)^2 + x/(1.09)^3 + x/(1.09)^4 + x/(1.09)^5 + x/(1.09)^6 + x/(1.09)^7 + x/(1.09)^8 = 140854.33

therefore x = 12771.87