Question

In: Accounting

The published sale price of a small apartment building comparable sale was $245,000. The buyer had...

The published sale price of a small apartment building comparable sale was $245,000. The buyer had mostly non-reported income and could not qualify for a standard mortgage. He agreed to purchase the property for $245,000 with the seller taking back a purchase-money mortgage of $175,000 at 7 percent for 30 years with monthly payments and a balloon payment in six years. The market interest rate for a property like this at the time of sale was a 9 percent with no points. What is the cash equivalent sales price, assuming the buyer would keep the financing in place for six years. (Round to the nearest $1000)

A. $245,000

B. $230,000

C. $200,000

D. $175,000

Solutions

Expert Solution

Price of property is $245000. However Principal amount of mortgage (P) is $175000. Therefore Amount paid in cash while purchasing property is $ 70000

Interest rate for 6 years is 7% per annum i.e. R= (7/12)% per month.

Tenure of loan is 30 years. therefore N (no of monthly installments) = 360

Therefore the equated monthly installment (EMI) comes to $1164

EMI = P x R((1+R)^N) / [(1+R)^N-1]

EMI = 175000 x [(7/12) (1+7/12)360 ] / [(1+7/12) 360-1]

EMI = 1164.

Therefore the buyer paid monthly installments for 6 years. Total payment = 72*1164= $ 83808

Amount outstanding at the end of 6th year will be $ 162235. This payment is made by the buyer one-time after 6th year.

Further, Interest rate prevailing in the market for such property is 9% at the time of purchase of property.

Therefore to find out cash equivalent sale price we need to compute present value of each future cash outflow till 6 years. Present Value Factor = 1/(1+R)N

A. Present value of $1164 per month = 1164 * [1- (1+R)-n] / R = 1164 * [1-(1+0.0075)-72] / 0.0075 = $ 64575

B. Present value of lumsum amount $ 162235 = 1 / (1+R)n =1/(1+0.0075)72 = 0.5839 * 162235 = $  94730

Total cash equivalent cost = Cash paid while purchasing property i.e. $ 70000 PLUS Present value of EMI of $1164 per month i.e. $ 64575 PLUS Present value of lumsum amount of $ 162235 paid at the end of year 6 i.e.

Total cash equivalent cost = $ 70000 +$ 64575 + $ 94730 = $ 229305 = $ 230000 (rounded off to $1000)

Conclusion : Cash Equivalent of $ 230000 is paid by the buyer to purchase property.


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