Question

Please answer all questions.

1. Your firm has decided to purchase a new $15,000 machine. You can pay now and take a 3 percent discount or pay $6,000 each year for the next three years. What is the interest rate at which the two alternatives are equal? Why?

2. A machine cost $10,000 and has a useful life of 5 years. If the interest rate is 8 percent how much must be saved every year to recover the cost of the investment?

3. Your firm requires returns of 18 percent per year. Should your firm buy a 3-year contract for $5,000 if it saves the company $200 a month? Why?

4. You borrow $4,500 to buy a car at 12% interest compounded monthly to be repaid over the next 4 years, what is your approximate monthly payment?

5. Using an interest table gradient series factor, write an equation to find the Present Worth (at Year 0) of the following series of payments when the interest is 4%:

Year	Net Cash Flow ($)
0	-1,000
1	500
2	600
3	700
4	800
5	900

6. Find the present worth for the problem above using both the equation and the summation of the present worth for each cash flow separately.

7. Maintenance on tools in a factory is expected to be $275 at the end of the first year and increase $50 each year for the following 7 years. What approximate present sum of money should be set aside now to pay the maintenance costs for the 8-year period, given that there is an 8% interest rate?

Answer 1

1.

If 3% discount is taken, then

Payment for the purchase = 15000*(1-3%) = $14550

If 3 annual installment of $6000 is taken,

Then,

Present value of payment = 6000*(1-1/(1+R)^3)/R

At R = 11%

Present value of the payment = $14662.29

At R = 12%

Present value of the payment = $14410.99

By applying the method of interpolation,

R = 11% + ((14662.29-14550)/( 14662.29-14410.99))*(12%-11%)

R = 11.44%

So, at the rate of 11.44%, both the payment methods will have the equal present value. So, both the methods become equal at 11.44%.

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