Terrie is thinking of buying a new home. Currently, she owns an older home that costs...

Terrie is thinking of buying a new home. Currently, she owns an older home that costs her approximately $35,000 a year. The cost of the new home is $320,000. She can obtain a $255,000 mortgage for 20 years at 3.5% interest. The home has homeowner’s association dues of $150 a month. Annual costs for property taxes, hazard insurance, and estimated landscaping/maintenance is approximately $1,250, $1,500, and $1,500. She estimates that she will live in the home for 10 years and resell it for $400,000. Terrie’s discount rate is 5%. Is this a good investment according to NPV? IRR? (12 points)

Expert Solution

Current Position

Annual cost associated with old home per annum = $35,000 p.a.

Net Present value of the costs associated with the old home is = 35,000 * PVAF(5%, 10) = 35,000 * 7.7217 = -270,259,50

Annual cost associated with new home per annum is $ 6,050 for years 1 to 10

Homeowner’s association dues = 150 * 12 = $ 1,800
Property taxes = $ 1,250
Hazard insurance = $ 1,500
Landscaping/maintenance = $1,500

Annual equal instalment payable on mortgage loan for 20 years = $ 255000 / PVAF(20y, 3.5%) = 255000/14.2124 = $ 17,942.08

Loan amount repayable at the end of 10th year = $ 17,942.08 * PVAF(10y, 3.5%) = $ 17,942.08 * 8.3166 = $149,217.1

year	cost of new home	Annual Costs	sale value	loan	loan amount remaining	Net cash flows	Present Value Factor 5%	Present Value
0	-3,20,000.00			2,55,000.00		-65,000.00	1	-65,000.00
1		-6,050.00		-17,942.08		-23,992.08	0.952381	-22,849.60
2		-6,050.00		-17,942.08		-23,992.08	0.907029	-21,761.52
3		-6,050.00		-17,942.08		-23,992.08	0.863838	-20,725.26
4		-6,050.00		-17,942.08		-23,992.08	0.822702	-19,738.34
5		-6,050.00		-17,942.08		-23,992.08	0.783526	-18,798.42
6		-6,050.00		-17,942.08		-23,992.08	0.746215	-17,903.26
7		-6,050.00		-17,942.08		-23,992.08	0.710681	-17,050.72
8		-6,050.00		-17,942.08		-23,992.08	0.676839	-16,238.78
9		-6,050.00		-17,942.08		-23,992.08	0.644609	-15,465.51
10		-6,050.00	4,00,000.00	-17,942.08	-1,49,217.10	2,26,790.82	0.613913	1,39,229.89
								-96,301.54

Net Present Value of the cash flows associated with new home is $ -96,301.54

Buying new home is preferred as net present value of costs of new home is less than NPV of cost of old home.

IRR

The present value of incremental cash flows becomes negative between 25% and 26%.

year	net cash flows (old home)	Net cash flows (new home)	Incremental Cash Flows	Present Value Factor 25%	NPV 25%	Present Value Factor 26%	NPV 26%
0		-65,000.00	-65,000.00	1.00000	-65000.00	1.00000	-65,000.00
1	-35,000.00	-23,992.08	11,007.92	0.80000	8806.34	0.79365	8,736.44
2	-35,000.00	-23,992.08	11,007.92	0.64000	7045.07	0.62988	6,933.69
3	-35,000.00	-23,992.08	11,007.92	0.51200	5636.06	0.49991	5,502.93
4	-35,000.00	-23,992.08	11,007.92	0.40960	4508.84	0.39675	4,367.40
5	-35,000.00	-23,992.08	11,007.92	0.32768	3607.08	0.31488	3,466.19
6	-35,000.00	-23,992.08	11,007.92	0.26214	2885.66	0.24991	2,750.95
7	-35,000.00	-23,992.08	11,007.92	0.20972	2308.53	0.19834	2,183.29
8	-35,000.00	-23,992.08	11,007.92	0.16777	1846.82	0.15741	1,732.77
9	-35,000.00	-23,992.08	11,007.92	0.13422	1477.46	0.12493	1,375.21
10	-35,000.00	2,26,790.82	2,61,790.82	0.10737	28109.58	0.09915	25,956.67
					1231.42		-1994.46

IRR = R1 + [NPV1 *(R2-R1) /(NPV1-NPV2)] = 25 + [1231.42 / 3225.89] = 25.382.

As the incremental cash flows of choosing new home is giving positive IRR new home is preferrred

jeff jeffy answered 1 year ago

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