Question

Suppose that you are contemplating an investment in an apartment building. Use the information provided below to answer the questions that follow: Type of Property: Apartment Building Number of Units: 30 Average Rent: $1,500 per unit per month Expected Growth in Rents: 5% per year Vacancy and Collection Losses: 5% of Potential Gross Income Other Income: $50 per unit per month Expected Growth in Other Income: 3% per year Operating Expenses: 35% of Effective Gross Income Capital Expenditures: 4% of Effective Gross Income Selling Expenses: 5% of Future Selling Price Going-Out Cap Rate: 6.5% Expected Purchase Price: $5.25 million Loan Terms: Loan Amount: 85% of purchase price Interest Rate: 4.5% per year with monthly payments and monthly compounding Amortization Term: 30 years a. What is the net present value of the before-tax unlevered cash flows if you assume a five-year holding period and a discount rate of 12%? b. What is the internal rate of return of the before-tax levered cash flows if you still assume a five-year holding period?

Answer 1

a..	0	1	2	3	4	5
a.Purchase price	-5250000
b.CAPEX(4%*(1+2))		-21600	-22680	-23814	-25005	-26255
c.Going-out value(Yr.5 Net income/6.5%) net of selling expenses(425570/6.5%*(1-5%))						6219869
1.Rental Income(Prev.30*1500*12)*(1.05)		540000	567000	595350	625118	656373
2.Vacancy & collection losses(Annual rent*5%)		-27000	-28350	-29768	-31256	-32819
3.Other income(Prev.50*30*12)*(1.03)		18000	18540	19096	19669	20259
4.Operating Expenses(35%*(1+2)		-179550	-188528	-197954	-207851.6	-218244	425570	(Net income for Yr.5)
5.Net before-tax Unlevered annual cash flows(a+b+c+1+2+3+4)	-5250000	329850	345982	362911	380674	6619184		(1+2+3+4)
6. PV at 12%(1/1.12^Yr.n)	1	0.89286	0.79719	0.71178	0.63552	0.56743
7. PV at 12%(5*6)	-5250000	294509	275815	258313	241925	3755903
8. NPV(sum of Row 7)	-423535

b..
Purchase price	5250000
Loan amt.*5%*5250000	4462500
Int. rate	4.50%	p.a.
ie.(4.5%/12)=	0.375%	p.m.

Mthly payment on the loan using the PV of annuity formula,
4462500=Mthly.pmt.*(1-1.00375^-360)/0.00375
Solving the above , we get the
Mthly pmt.=22611

Amortisation of Loan (for the first 5 years)
Mth.	Mthly pmt.	Tow. Int.	Tow. Loan	Loan Bal.
1	2	3=Prev.5*0.375%	4=2-3	5=Prev.5-4
0				4462500
1	22611	16734.38	5876.625	4456623
2	22611	16712.34	5898.662	4450725
3	22611	16690.22	5920.782	4444804
4	22611	16668.01	5942.985	4438861
5	22611	16645.73	5965.271	4432896

b..	0	1	2	3	4	5
a.Purchase price	-5250000
b.CAPEX(4%*(1+2))		-21600	-22680	-23814	-25005	-26255
c.Going-out value(Yr.5 Net income/6.5%) net of selling expenses(408924/6.5%*(1-5%))						5976582
1.Rental Income(Prev.30*1500*12)*(1.05)		540000	567000	595350	625118	656373
2.Vacancy & collection losses(Annual rent*5%)		-27000	-28350	-29768	-31256	-32819
3.Other income(Prev.50*30*12)*(1.03)		18000	18540	19096	19669	20259
4.Operating Expenses(35%*(1+2)		-179550	-188528	-197954	-207852	-218244
5.Loan Interest payments		-16734	-16712	-16690	-16668	-16646	408924	(Net income for Yr.5)
6.Net before-tax levered annual cash flows(a+b+c+1+2+3+4+5)	-5250000	313115.5	329270.1	346220.5	364006.3	6359251		(1+2+3+4+5)
6. PV at 12%(1/1.12^Yr.n)	1	0.89286	0.79719	0.71178	0.63552	0.56743
7. PV at 12%(5*6)	-5250000	279567	262492	246433	231333	3608410
8. NPV(sum of Row 7)	-621765

a.NPV of Unlevered cash flows	-423535
b.NPV of levered cash flows	-621765