Question

Stu can purchase a house today for $110,000, including the cost of some minor repairs. He expects to be able to resell it in one year for $129,000 after cleaning up the property. At a discount rate of 5.5 percent, what is the expected net present value of this purchase opportunity?

Answer 1

Solution :

The Net Present Value of a purchase opportunity is the present value of its future cash flows minus its initial cash outlay.

Thus, Net Present Value = Present value of future Cash Inflows - Initial Cash outlay

As per the information given in the question we have

Initial Cash outlay = $ 110,000                                                                    

Single future cash inflow = $ 129,000 ; Year of cash inflow = 1   ; Discount rate = 5.5 %

The present value factor at 5.5 % discount rate in year 1 = PVF ( 5.5 % , 1 ) = 0.947867

Thus the Present value of future cash inflow = $ 129,000 * PVF( 5.5 %, 1 )

= $ 129,000 * 0.947867

= $ 122,274.8430

The present value of Future cash Inflow at the end of Year 1 = $ 122,274.8430

We know that NPV is = Present value of future Cash Inflows - Initial Cash outlay

Applying the available information we have NPV =

= $ 122,274.8430 - $ 110,000

= $ 12,274.8430

= $ 12,275 ( when rounded off to the nearest whole number )

Thus the expected net present value of this purchase opportunity = $ 12,275

Note :

Formula PV for Year 1 = 1/(1+Discount rate)ⁿ where n =1 ;

(1+Disc. rate) is raised to the power of n = No. of yrs.

Thus PVF(5.5 %,1) = 1 /( 1 + 0.055) ¹

= 1/ 1.055 = 0.947867