Lucy bought a house that costs $100,000. She financed it with an 80% LTV mortgag

Question

Lucy bought a house that costs $100,000. She financed it with an 80% LTV mortgage. The mortgage is a 30 year fully amortizing FRM with annual compounding and annual payments. Lucy’s annual cost of ownership net of tax savings is exactly equal to the annual rent she would have paid to live in the same house. Lucy will sell the house 30 years after purchase. Suppose the house price grows 4.5% annually (compounded annually). Buying costs are 5% of the purchase price of the house. Selling costs are 8% of the selling price of the house.

I just need the answer to 31 and 32 please. The other answers are correct. (Needs to be correct to the cent)

Thanks!

Lucy bought a house that costs $100,000. Sho financed it with an 80% LTV mortgage. The mortgage is a 30 year fully amortizing FRM th annual compounding and annual payments. Lucy's annuei cost of ownership net of tax savings is exactly equal to the annual rent she would have paid to ive in the same house. Lucy will sell the house 30 ears after purchase. Suppose he house pr e grows 4 5% annually compounded annual Bu in costs are 5% o he purchase pro e of the house. Sel ng costs are 8 house. 2. (a) What's the sale price of the house in 30 years? 374531.81 ofthese ng pnce or the QUESTION 29 3 points Saved Continued) 2. (b) What's Lucy's house sale cash flowlafter expenses)? 344569.27 QUESTION 30 3 points Saved (Continued) 2. (c) What's Lucy's initial cash flow when she purchased the house? (negative number) -2500 QUESTION 31 5 points Save Answer (Continued) 2, (d) what's the NPV for Lucy's buy vs lease decision if her annual discount rate is 5%? QUESTION 32 5 points Save Answer (Continued) 2. (e) What is Lucy's annual IRR from owning net of leasing?

Explanation / Answer

Answer to 30 is wrong. It must be 20% of $100,000 + 5%*$100,000 = $25,000 and NOT $2,500. Kindly correct that as well.

31) SInce Lucy;s annual cost of ownership is exactly same as the amount of rent she would have paid, the only cash out flow for lucy is $25000 at beginning and will receive $344,569.27 at the end of 30 years (house proceeds)

So 344,569.27 discounted @5% for 30 years is $79,725.56

Now NPV = 79,725.56 - $25,000 = $54,725.56

Now with these 2 cash flows CF0 = -25000; CF30 = 344569.27, Calculate IRR = 9.14%

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