Raul Martinas, professor of languages at Eastern University, owns a small office

Question

Raul Martinas, professor of languages at Eastern University, owns a small office building adjacent to the university campus. He acquired the property 10 years ago at a total cost of $541,000—$53,000 for the land and $488,000 for the building. He has just received an offer from a realty company that wants to purchase the property; however, the property has been a good source of income over the years, so Professor Martinas is unsure whether he should keep it or sell it. Assume that Professor Martinas requires a 15% rate of return. His alternatives are:

Alternative 1: Keep the property. Professor Martinas’ accountant has kept careful records of the income realized from the property over the past 10 years. These records indicate the following annual revenues and expenses:


Rental receipts $133,000
Less building expenses:
Utilities $24,900
Depreciation of building 15,100
Property taxes and insurance 17,000
Repairs and maintenance 8,100
Custodial help and supplies 38,800 

Total Building Expenses 103,900
Net operating income 29,100


Professor Martinas makes a $12,200 mortgage payment each year on the property. The mortgage will be paid off in 8 more years. He has been depreciating the building by the straight-line method, assuming a salvage value of $110,500 for the building which he still thinks is an appropriate figure. He feels sure that the building can be rented for another 15 years. He also feels sure that 15 years from now the land will be worth three times what he paid for it.

Alternative 2: Sell the property. A realty company has offered to purchase the property by paying $177,000 immediately and $26,300 per year for the next 15 years. Control of the property would go to the realty company immediately. To sell the property, Professor Martinas would need to pay the mortgage off, which could be done by making a lump-sum payment of $91,600.

To determine the appropriate discount factor(s) using tables, click here to view Exhibit 12B-1 and Exhibit 12B-2. Alternatively, if you calculate the discount factor(s) using a formula, round to three (3) decimal places before using the factor in the problem.

Required:
(a)
Calculate the present value of cash flows if he keeps the property. (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)

Present value of cash flows $

(b)
Calculate the present value of cash flows if he sells the property. (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)

Present value of cash flows $

(c) Would you recommend he keep or sell the property?

Explanation / Answer

Prof Martinas case : Alt 1: We will calculate the PV of Future cash flows of next 15 Yrs. a. PV of Annuity (Net Op Income+Dep written back - Mortgae payment) for n=8 yrs using Kd=i=15%. b. PV of Annuity (Net Op Income+Dep written back for next n=7 yrs) ie at T8 & then discounting it to present by 8 yrs to T0 with i=15%. c. PV of Salvage value of $110,500, n=15yrs, Kd=15% d. PV of Land (Value 3*$53,000 = $159,000), n=15yrs,Kd=15% Lets calculate the above now. a. PV of $29,100+$15,100-$12,000 = $32,200 =PMT Present value of annuity PVA = PMT(PVIFAi,n). So PVA = PMT*(1/i - 1/(i(1+i)^n)) So we get PVA = PMT*(1/15% -1/(15%*(1+15%)^8)) ie PVA = PMT*(6.6667-2.1793) =PMT*4.1874 = 32,200*4.1874 = $144,494.28 So PVA1 = $144,494.28 b. PV of Annuity (Net Op Income+Dep written back = 29100+15100=44200=PMT for next n=7 yrs) ie at T8 & then discounting it to present by 8 yrs to T0 with i=15%. Present value of annuity PVA = PMT(PVIFAi,n). So PVA = PMT*(1/i - 1/(i(1+i)^n)) So we get PVA = PMT*(1/15% -1/(15%*(1+15%)^7)) ie PVA = PMT*(6.6667-2.5063) =PMT*4.1604 = 44,200*4.1604 = $183,889.68 So PVA2 = $183,889.68 PV of PVA2 for n=8 & Kd=15% is =PVA2/(1+Kd)^n = 183,889.68/(1+15%)^8 = $60,113.86 So PV=$60,113.86 c. PV of Salvage value of $110,500, n=15yrs, Kd=15% PV = FV/(1+Kd)^n = 110500/(1+15%)^15 = $13,579.84 d. PV of Land (Value 3*$53,000 = $159,000), n=15yrs, Kd=15% PV = FV/(1+Kd)^n = 159,000/(1+15%)^15 = $19,540.22 So PV of CFs of Alt 1 = Sum of a+b+c+d = $144,494.28+60,113.86+13579.84+19540.22 = $237,728.20......(A) Alt 2: We will calculate the PV of Future cash flows of next n=15 Yrs. a. Lump sum of $177,000 as down payment b. PV of Annuity (annual payment) of $26,300 for n=15yrs using i=15% c. Deduct from (a+b), mortgae closure of $91,600 a. PV is same as downpayment = $177,000 b. Present value of annuity PVA = PMT(PVIFAi,n). So PVA = PMT*(1/i - 1/(i(1+i)^n)) So we get PVA = PMT*(1/15% -1/(15%*(1+15%)^15)) ie PVA = PMT*(6.6667-0.8193) =PMT*5.8474 = 26300*5.8474 = $153,786.62 So PV of CFs for Alt 2 = $177,000+153,786.62-91,600 = $239,186.62......(B) From A&B above, we see that differnce in Cfs is only $1458.42. So it now depends on the Risk appetite & the certainity of Rental CFs & expenses. We all know that Future is uncertain. The Rentals can come down as happened during the Market crash in 2008. As difference between two options is very small, Prof is better-off with Alt 2 where he is assured of future CFs for 15 Yrs.

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.