Question

1) You are considering an investment that will pay you $12,000 the first year, $13,000 the second year, $17,000 the third year, $19,000 the fourth year, $23,000 the fifth year, and $28,000 the sixth year (all payments are at the end of each year). What is the maximum you would be willing to pay for this investment if your opportunity cost is 11%?

3)How much would you be willing to pay for an investment that will pay you and your heirs $16,000 each year in perpetuity if your opportunity cost is 6%?

ONLY ANSWER THIS TWO QUESTIONS! MUST DO ON EXCEL AND SHOW WORK:

Rework Question 1 assuming an opportunity cost of 11% with daily compounding.

Rework question 3) if you want the payments to grow by 2% indefinitely. ( first payment in 16000 in year 1)

Answer 1

1. The amount that I will be willing to pay for this investment = sum of present value of all future payments which will be discounted at 11%

Thus amount = 12,000/1.11 + 13,000/1.11^2 + 17,000/1.11^3 + 19,000/1.11^4 + 23,000/1.11^5 + 28,000/1.11^6

= $74,927.37

Year	CF	1+r	PVIF	PV
1	12,000.00	1.11	0.9009	10,810.81
2	13,000.00		0.8116	10,551.09
3	17,000.00		0.7312	12,430.25
4	19,000.00		0.6587	12,515.89
5	23,000.00		0.5935	13,649.38
6	28,000.00		0.5346	14,969.94
			Total	74,927.37

3. Here we have to compute present value of perpetuity. PV = amount per period/r = 16,000/6% = $266,666.67

Question 1 Reworked:

In case of daily compounding n = 365. Thus effective rate = (1+(11%/365))^365

= 11.6260%

Thus the cash flows will be discounted at the rate of 11.6260% and amount thai I will be willing to pay is:

Year	CF	1+r	PVIF	PV
1	12,000.00	1.116260	0.8958	10,750.19
2	13,000.00		0.8025	10,433.09
3	17,000.00		0.7190	12,222.31
4	19,000.00		0.6441	12,237.50
5	23,000.00		0.5770	13,270.95
6	28,000.00		0.5169	14,473.28
			Total	73,387.31

Hence I will be willing to pay $73,387.31

3) Annual amount = $16,000. This is the payment made at the end of year 1.

Thus I will be willing to pay: Annual amount/(r-g)

= 16,000/6%-2%)

= $400,000