Question

Larkspur, Inc., a manufacturer of low-sugar, low-sodium, low-cholesterol TV dinners, would like to increase its market share in Western Canada. In order to do so, Larkspur has decided to locate a new factory in Kelowna, B.C. Larkspur will either buy or lease a site, depending upon which is more advantageous. The site location committee has narrowed down the available sites to the following three buildings.

Building A: Purchase for a cash price of $607,000, useful life 25 years.

Building B: Lease for 25 years with annual lease payments of $72,500 being made at the beginning of the year.

Building C: Purchase for $663,000 cash. This building is larger than needed; however, the excess space can be sublet for 25 years at a net annual rental of $7,500. Rental payments will be received at the end of each year. Larkspur, Inc. has no aversion to being a landlord.

Click here to view the factor table PRESENT VALUE OF 1.
Click here to view the factor table PRESENT VALUE OF AN ANNUITY OF 1.
Click here to view the factor table PRESENT VALUE OF AN ANNUITY DUE.

Calculate the net present value of three buildings, assuming a 12% cost of funds. (For calculation purposes, use 5 decimal places as displayed in the factor table provided. Round final answers to 0 decimal places, e.g. 5,275.)

		Net present value
Building A		$enter a dollar amount rounded to 0 decimal places
Building B		$enter a dollar amount rounded to 0 decimal places
Building C		$enter a dollar amount rounded to 0 decimal places

In which building would you recommend that Larkspur, Inc. locate?

Answer 1

PV of Building A :

PV of Building A= $607,000

PV of Building B:

PV = CF1 + CF2/(1+r) + CF2/(1+r)² + CF3/(1+r)³ ….. CFt/(1+r)^t-1

Where, CFt is cash flow at beginning of time=t

r is discount rate

Annual lease payment = $72,500

t=25 years

r = 12%

Year (t)	Annual lease Payment (CF)	Discounting factor (D) =(1/1+r)t-1	PVt = (CF)*(D)
1	72500	1	72500.00
2	72500	0.89286	64732.14
3	72500	0.79719	57796.56
4	72500	0.71178	51604.07
5	72500	0.63552	46075.06
6	72500	0.56743	41138.45
7	72500	0.50663	36730.76
8	72500	0.45235	32795.32
9	72500	0.40388	29281.53
10	72500	0.36061	26144.23
11	72500	0.32197	23343.06
12	72500	0.28748	20842.02
13	72500	0.25668	18608.94
14	72500	0.22917	16615.13
15	72500	0.20462	14834.94
16	72500	0.18270	13245.48
17	72500	0.16312	11826.32
18	72500	0.14564	10559.21
19	72500	0.13004	9427.87
20	72500	0.11611	8417.74
21	72500	0.10367	7515.84
22	72500	0.09256	6710.57
23	72500	0.08264	5991.58
24	72500	0.07379	5349.63
25	72500	0.06588	4776.45

PV of Building B = Sum of PVt = $636,862.90

PV of Building C:

Initial outflow = $663,000

Annual rental received for 25 years = $7,500

PV = CF1/(1+r) + CF2/(1+r)² + CF2/(1+r)³ + CF3/(1+r)⁴ ….. CFt/(1+r)^t

Where, CFt is cash flow at end of time=t

r is discount rate

PV of annual rental received for 25 years:

Year (t)	Annual Rental (CF)	Discounting factor (D) =(1/1+r)t	PVt= (CF)*(D)
1	7500	0.89286	6696.43
2	7500	0.79719	5978.95
3	7500	0.71178	5338.35
4	7500	0.63552	4766.39
5	7500	0.56743	4255.70
6	7500	0.50663	3799.73
7	7500	0.45235	3392.62
8	7500	0.40388	3029.12
9	7500	0.36061	2704.58
10	7500	0.32197	2414.80
11	7500	0.28748	2156.07
12	7500	0.25668	1925.06
13	7500	0.22917	1718.81
14	7500	0.20462	1534.65
15	7500	0.18270	1370.22
16	7500	0.16312	1223.41
17	7500	0.14564	1092.33
18	7500	0.13004	975.30
19	7500	0.11611	870.80
20	7500	0.10367	777.50
21	7500	0.09256	694.20
22	7500	0.08264	619.82
23	7500	0.07379	553.41
24	7500	0.06588	494.12
25	7500	0.05882	441.17

PV of annual rental received for 25 years = Sum of PVt = $58,823.54

PV of Building C = 663000-58823.54 = $604,176.46

	Net Present Value
Building A	$607,000
Building B	$636,863
Building C	$604,176

Larkspur, Inc. should locate itself in Building C as its net present value is lowest of all.