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House A costs $100,000 with annual energy costs of $1,800 per year. House B costs $110,000...

House A costs $100,000 with annual energy costs of $1,800 per year. House B costs $110,000 with annual energy costs of $600 per year. You must borrow the money to purchase the houses at an interest rate of 7% per year for a 30-year mortgage, and that energy costs will escalate 1% per year.

a) What would be the simple payback of investing in House B compared to House A? Is this a good investment?

b) What are the annualized owning (mortgage + energy) costs of each house? What is the net annualized savings of House B compared to House A? Is this a good investment?

Expert Solution

a. Simple payback: Cost of house A: = 7%*100,000 + 1800 =7000+1800 = $8,800

Simple payback for house B:= 7%*110,000 + 600 = $8,300

Since B has a lower payback, B is a better a better investment than A

b The monthly payment for a 30 year mortgage is calculated using =PMT(rate,nper,pv) function in excel .

For house A, rate = 0.07/12, nper = 30*12 and pv =100,000

Monthly payment for house A =PMT(0.07/12,30*12,100000) = $665.30

So, annual mortgage payments = $665.30*12 = 7,983.60

Energy cost (annual) = 1,800

Annual cost of owning for house A = 7983.6+1800 = $9,783.60

For house B, rate = 0.07/12, nper = 30*12 and pv =110,000

Monthly payment for house B =PMT(0.07/12,30*12,110000) = $731.83

So, annual mortgage payments = $731.83*12 = 8,781.96

Energy cost (annual) = 600

Annual cost of owning for house B = 8781.96+600 = $9,381.96

Net annualized savings for House B = Annualized cost of owning of A - Annualized cost of owning of B = $9,783.60 -$9,381.96 = $401.64

jeff jeffy answered 2 years ago

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