Question

PROBLEMS 87 ufactures or pumps nts. If the on in a 5760.000 return did company spends $75.000 per year on new equipment, how many years will it take to reduce the fund to less than $75.000 at an interest rate of 10% per year? 2.57 ent? reased to d. What estment? An A&E firm is considering purchasing the building it currently occupies under a long- term lease because the owner of the build- ing suddenly put it up for sale. The building is being offered at a price of $170,000. Since the lease is already paid for this year, the next annual lease payment of $30,000 isn't due until the end of this year. Because the A&E firm has been a good tenant, the owner has offered to sell to them for $160,000. If the firm purchases the build- ing with no down payment, how long will it be before the company recovers its invest- ment at an interest rate of 12% per year?! in pow- and pur- nough to building business nual in- xpenses mount to urn will the cash ears are 2.58 An engineer who invested very well plans to retire now because she has $2,000,000 in her ORP account. How long will she be able to withdraw $100,000 per year (be- ginning 1 year from now) if her account earns interest at a rate of 4% per year? ompany

2.57

Answer 1

(2.57)

Actual purchase price = $160,000

Annual income = $30,000

Discounted payback period (DPBP) is the time by when cumulative discounted cash flows becomes zero.

Year	Cash flow ($)	PV Factor @12%	Discounted Cash Flow ($)	Cumulative Discounted Cash Flow ($)
0	-1,60,000	1.0000	-1,60,000	-1,60,000
1	30,000	0.8929	26,786	-1,33,214
2	30,000	0.7972	23,916	-1,09,298
3	30,000	0.7118	21,353	-87,945
4	30,000	0.6355	19,066	-68,880
5	30,000	0.5674	17,023	-51,857
6	30,000	0.5066	15,199	-36,658
7	30,000	0.4523	13,570	-23,087
8	30,000	0.4039	12,116	-10,971
9	30,000	0.3606	10,818	-153
10	30,000	0.3220	9,659	9,507

DPBP lies between years 9 and 10.

DPBP = 9 + (Absolute value of cumulative discounted cash flow, year 9 / Discounted cash flow, year 10)

= 9 + (153 / 9,659)

= 9 + 0.02

= 9.02 years