Question

On January 1, 2017, Wood Corporation leases a piece of equipment from Prior Corporation and properly accounts for the equipment as a finance lease. Under the agreement, Wood will make 7 annual payments of $750,000 each January 1st. At the end of 7 years, Wood has the option of buying the equipment for $200,000, when the estimated fair value will be $400,000. If Wood's incremental borrowing rate is 7%, what is the present value of the minimum lease payments?

$4,574,004.64

$4,166,517.00

$4,449,454.69

None of the above

Answer 1

Formula PV of annuity due can be used to compute present value of 7 annual payments as:

PV = C x PVIFAD (i, n)   

C = annual cash payment = $ 750,000

i = Rate of interest = 7 %

n = Number of periods = 7

PV of annual payments = $ 750,000 x PVIFAD (7 %, 7)

                                 = $ 750,000 x [1 – (1+0.07)^-7/0.07] x (1+0.07)

                                 = $ 750,000 x [1 – (1.07)^-7/0.07] x (1.07)

                             = $ 750,000 x [(1 – 0.622749741884591)/0.07] x (1.07)

                             = $ 750,000 x (0.377250258115409/0.07) x (1.07)

                            = $ 750,000 x 5.3892894016487 x 1.07

                            = $ 4,324,904.74482308

Present value of buying cost at the end of 7 years can be computed using formula for PV of single sum as:

PV = FV/ (1+r) ⁿ

PV of buying cost = $ 200,000/ (1+0.07)⁷

                                = $ 200,000/ (1.07)⁷

                                = $ 200,000/1.60578147647843

                                = $ 124,549.948376918

Total PV = PV of annual payments + PV of buying cost

               = $ 4,324,904.74482308 + $ 124,549.948376918

               = $ 4,449,454.693199998 or $ 4,449,454.69

Present value of minimum lease payment is $ 4,449,454.69

Hence option “$ 4,449,454.69” is correct answer.