Question

The monthly income from a piece of commercial property is

​$1,400

​(paid as a lump sum at the end of the​ year). Annual expenses are

​$2,000

for upkeep of the property and

​$900

for property taxes. The property is surrounded by a security fence that cost​ $4,000 to install four years ago. Assume 52 weeks in a year and​ end-of-year cash flows.

a. If

i=15​%

per year​ (the MARR) is an acceptable interest​ rate, how much could you afford to pay now for this property if it is estimated to have a​ re-sale value of

​$140,000

ten years from​ now?

b. Choose the correct cash flow diagram for this situation. Use the viewpoint of the buyer.

c. Based on this​ situation, give examples of opportunity costs.

d. Based on this​ situation, give examples of fixed costs.

e. Based on this​ situation, give examples of sunk costs.

f. If the

15​%

interest had been a nominal interest​ rate, what would the corresponding effective annual interest rate have been with​ bi-weekly (every two​ weeks) compounding?

Answer 1

a) Property price to be paid today = $104,367

	Annual income	16800
	Annual expense for upkeep of property	-2000
	Annual property tax	-900
	Total annual expense	-2900
	Total annual cash flow	13900
	Minimum acceptable rate of return	15%
	At MARR as discount rate, NPV would be zero
	Property re-sale value	140000
Year	Cash flow	Discount factor at 14%	Present value CF
0	X (payment for the property)	1.000	X
1	13,900	0.870	12,087
2	13,900	0.756	10,510
3	13,900	0.658	9,139
4	13,900	0.572	7,947
5	13,900	0.497	6,911
6	13,900	0.432	6,009
7	13,900	0.376	5,226
8	13,900	0.327	4,544
9	13,900	0.284	3,951
10	153,900	0.247	38,042
		NPV (at 14% discount rate)	0
	Property value to be paid today		-104,367

Excel formula:

c) Opportunity cost of capital = MARR = 14%

d) Fixed cost of is annual expense for upkeep of property and property tax = 2000 + 900 = $2,900

e) Sunk cost = cost of security fencing paid 4 years ago = $4,000

f) Effective annual interest (bi weekly compunding) = (1+15%/26)^(26) -1 = 16.1%