Question

4. (40%) You have two office-block proposals. You initially intended to invest $300,000 in the building and then sell it at the end of the year for $400,000. Under the revised proposal, you planned to rent out the offices for 3 years at a fixed annual rent of $20,000 and then sell the building for $400,000. a). Calculate the IRR for the initial proposal; b). Calculate the IRR for the revised proposal; c). Which proposal should be chosen based on the IRRs of the proposals? d). Calculate the crossover rate of initial and revised proposals; e). Suppose that you use NPV rule to rank these two proposals. Which proposal should be chosen if the appropriate discount rate is 5%? f). Explain why you have same (different) selection(s) in question c) and d).

Ans: a) IRR=33.33%

b)please solve b with calculations details (16.16%)

c) The initial pro should be chosen as it has a higher IRR

d)Please draw the graph to show where is cross over rate

e)Please solve

f)Please explain

Answer 1

Answer :-

4a )  

Given
Initial investment = $ 300000 ( Year 0)
Selling after 1 year
Selling price = $ 400000
IRR is the discount rate at which the NPV is zero

0 = - $ 300000 + [ $ 400000 / (1+ IRR)]
$ 400000 / (1+IRR) = $ 300000
1 + IRR = $ 400000 / $ 300000
1+IRR = 1.33
IRR = 1.3333 - 1
IRR = 0.3333 = 33.33%

4b)

Given

Initial investment = $ 300000
Rent = $ 20000 / year for 3 years
Selling after 3 years = $ 400000

IRR is the discount rate at which the NPV is zero
0 = - $ 300000 + $ 20000 / (1+IRR) + $ 20000 / (1+IRR)² + $ 20000 / (1+IRR)³ + $ 400000 / (1+IRR)³

Calculating IRR = 16.16 %

4c)

Based on the IRR the proposals with higher IRR should be selected

Therefore the initial  proposal with IRR = 33.33% should be selected instead of revised proposal with IRR of 16.16%.

4d)

Crossover rate of the initial proposal and revised proposal = 7.796%

Year	Initial Project (IP)	Revised Proposal (RP)	IP - RP
1	- $ 300000	- $ 300000	$ 0
2	+ $ 400000	+ $ 20000	$ 380000
3	$ 0	+ $ 20000	-$ 20000
4	$ 0	+ $ 420000	- $ 420000
IRR	33.33%	16.16%	7.796 %

cross over Rate 33,33% IRR(IP) 7.7964. A cost of (IRR) IRR(RP) (PN) 16.16%

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