Question

You are considering the purchase of a parking deck close to your office building. The parking deck is a​ 15-year old structure with an estimated remaining service life of 25 years. The tenants have recently signed​ long-term leases, which leads you to believe that the current rental income of​$250,000 per year will remain constant for the first five years. Then the rental income will increase by 10​% for every​ five-year interval over the remaining asset life.​ Thus, the annual rental income would be ​$275,000 for years 6 through​ 10, ​$302,500 for years 11 through​ 15, ​$332,750 for years 16 through​ 20, and ​$366,025 for years 21 through 25. You estimate that operating​ expenses, including income​ taxes, will be ​$71,000 for the first year and that they will increase by ​$4,000 each year thereafter. You estimate that razing the building and selling the lot on which it stands will realize a net amount of ​$180,000 at the end of the​ 25-year period. If you had the opportunity to invest your money elsewhere and thereby earn interest at the rate of 14​% per​ annum, what would be the maximum amount you would be willing to pay for the parking deck and lot at the present​ time?

Click the icon to view the interest factors for discrete compounding when i=14​% per year. The maximum amount you would be willing to pay for the parking deck and lot at the present time is

​$______? thousand. ​(Round to the nearest whole​ number.)

Answer 1

We will have to calculate the PW of the net cash flow here. The interest rate is 14% and duration of 25 years.

PW = Cash Flow / (1+Interest Rate)^Duration

The rental income is increasing by 10% every 5 years so it has 5 segments

Year 1 to 5

250000 * (1 / (1.14 ^ n)

219298.25 + 192366.88 + 168742.88 + 148020.07 + 129842.17
= 858270.24

Year 6 to 10

275000 * (1 / (1.14 ^ n)

= 490334.54

We can calculate the PW for other segments of rental income in the same manner

PW of total rental income
858270.24 + 490334.54 + 280130.83 + 160040.29 + 91431.91
= 1880207.81

Now we will calculate the PW of cost

The first year cost is $71000 and it has constant gradient of $4000 each year.

71000 * (P/A, 14%, 25) + 4000 * (P/G, 14%, 25)

(71000 * 6.8729 ) + (4000 * 42.3441)
= 487975.90 + 169376.40
= 657652.30

PW of the sell value at the end of 25th year

180000 / (1.14 ^ 25) = 6802.23

Net Present Value

1880207.81 + 6802.23 - 657652.30

= 1229657.74

The maximum amount paybale is $1229658

I have added the cash flow and PW table also.

Year	Rental Income	Expenses	Net Cash Flow	PW @ 14%
1	250000	71000	179000	157017.54
2	250000	75000	175000	134656.82
3	250000	79000	171000	115420.13
4	250000	83000	167000	98877.41
5	250000	87000	163000	84657.09
6	275000	91000	184000	83827.92
7	275000	95000	180000	71934.72
8	275000	99000	176000	61698.39
9	275000	103000	172000	52891.37
10	275000	107000	168000	45316.96
11	302500	111000	191500	45312.23
12	302500	115000	187500	38917.33
13	302500	119000	183500	33409.73
14	302500	123000	179500	28667.94
15	302500	127000	175500	24586.93
16	332750	131000	201750	24793.39
17	332750	135000	197750	21317.39
18	332750	139000	193750	18321.22
19	332750	143000	189750	15739.45
20	332750	147000	185750	13515.49
21	366025	151000	215025	13724.20
22	366025	155000	211025	11814.82
23	366025	159000	207025	10167.43
24	366025	163000	203025	8746.48
25	366025	167000	199025	7521.19

PW of the sell value at the end of 25th year

180000 / (1.14 ^ 25) = 6802.23

NPW = 1222853.58 + 6802.23
= 1229655.81 or 1229656