Question

1a. If the present value of $157 is $143, what is the discount factor? (Round your answer to 4 decimal places.)

b. If that $157 is received in year 5, what is the interest rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

2. Suppose you own a small company that is contemplating construction of a suburban office block. The cost of buying the land and constructing the building is $720,000. Your company has cash in the bank to finance construction. Your real estate adviser suggests that you rent out the building for two years at $31,000 a year and predicts that at the end of that time you will be able to sell the building for $848,000.

Thus there are now two future cash flows--a cash flow of C₁ = $31,000 at the end of year 1 and a further cash flow of C₂ = ($31,000 + 848,000) = $879,000 at the end of the second year.

a. Calculate the NPV of the office building venture at interest rates of 6, 11, and 16%. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Net Present value at 5%

Net Present value at 10%

Net Present value at 15%

b. At what discount rate (approximately) would the project have a zero NPV? Check your answer by calculating the NPV at your approximate rate; it should be close to zero. (Enter your answer as a percent rounded to the nearest whole number.)

Answer 1

1.a.	Discount factor if PV of $157 is $143
		=(157/143)-1	0.07692308
1.b.	interest rate if $157 is received after 5 years
		=(157/143)^(1/5)-1	0.01886
2.a.	Computation of NPV of the office building
			Y0	Y1	Y2	NPV
		Discount rate @6%	1.000	0.943	0.890
		Cash flows	-720000	31000	879000
		PV of Cash flows	-720000	29245.28302	782306.8708	91552.15
			Y0	Y1	Y2	NPV
		Discount rate @11%	1.000	0.901	0.812
		Cash flows	-720000	31000	879000
		PV of Cash flows	-720000	27927.92793	713416.1188	21344.05
			Y0	Y1	Y2	NPV
		Discount rate @16%	1.000	0.862	0.743
		Cash flows	-720000	31000	879000
		PV of Cash flows	-720000	26724.13793	653240.1902	-40035.7
2.b.		Discount rate at which NPV is 0	=(879000/(1+IRR)^2)+(31000/(1+IRR)) -720000			13%