Question

Magna Charter has been asked to operate a Beaver bush plane for a mining company exploring in Yukon. Magna will have a 1-year contract with the mining company and expects that the contract will be renewed after 1 year, for the remaining 4 years of the exploration program. If the mining company renews after 1 year, it will commit to use the plane for 4 more years. Magna Charter has the following choices:

(1) Buy the plane for $500,000

(2) Arrange a 5-year, non-cancellable, net financial lease at a rate of $75,000 per year, paid in advance

Assume that the CCA rate is 25% and Magna has many other airplanes in its asset pool. The first CCA deduction is made at the end of the first year. The company’s tax rate is 35%. The weighted-average cost of capital for the bush plane business is 14%, but Magna can borrow at 9%.

Ms. Magna thinks the plane will be worth $300,000 after 5 years. She also thinks that there is a 20% chance that the contract will not be renewed at year 1. If the contract is not renewed, the plane will have to be sold on short notice for $400,000.

If Magna Charters takes the 5-year financial lease and the mining company cancels at year 1, Magna can sublet the plane, that is, rent it out to another user. Magna must cover the operating costs of the plane. Assume that the operating costs are identical whether Magna buys or leases the plane.

Calculate the NPVLease ( or NAL). Show all of your work. Should they lease or buy the plane?

Answer 1

Expected NPV of lease if company buys the plane

Purchase price now = $ 500000

If contract renewes:

If contract gets renewed after 1 year (probability =80%), plan will be sold after 5 year at $300000 capital gain tax on sale will be =( sale - WDV after 5 years)× tax rate

WDV after 5 year = cost×(1-CCA rate)^5 = 500000×(1-.25)^5= $118652.34

Captain gain tax= (300000-118652.34)×.35= $63471.68

After tax cashflows from sale at time 5 = 300000-63471.68= $236528.32

To buy the plan now it will have to borrow from bank at 9% p.a. the annual loan payment is given by

L= E(1-(1+r)^-p)/r

Where

L = loan taken = $500000

r=9%

p = 5 years

E= annual loan payment = ???

Therefore

500000=E(1-1.09^-5)/.09

Solving for E we get E= $128546.23

Now the NPV in this case is given by

NAL = PV of annual instalments- PV of DTS -PV of ITS - PV after tax sale of plan all @Kc i.e.14%

PV of instalments = E(1-(1+Kc)^-p)/Kc = 128546.23(1-1.14^-5)/.14 = $441309.62

PV of DTS = PV of depreciation tax shield since we are following written down value(WDV) method on CCA.

Hence PV of DTS= (DTS/(Kc+d))×(1-((1-d)/(1+Kc))^p)

Where

DTS= depreciation tax shield in first year = 500000×.25×.35=$43750

Kc = 14%

d= 25%

p= 5

PV of DTS= (43750/(.14+.25)/(1-(.75/1.14)^5) =$98353.52

PV of ITS = present value of interest tax shield

Since this loan is on Equated payment basis then

PV of ITS = [ PVAF(Kc,p) -{PVIF(r,p) - PVIF(Kc,p)}/(Kc -r)]×E×tax rate

Where

Kc = 14%

r=9%

E= 128546.23

Tax rate = 35%

PVAF(kc,p) = (1-(1+Kc)^-p)/Kc = (1-1.14^-5)/.14= 3.433

PVIF(r,p) = 1/(1+r)^p = 1/1.09^5 = .6499

PVIF(Kc,p)= 1/(1+Kc)^p = 1/1.14^5= .5194

PV of ITS = [3.433-(.6499-.5194)/(.14-.09)]×128546.23×35% = 37027.74

PV of after tax sales= 236528.32/1.14^5 = 122845.40

NAL= 441309.62-98353.52-37027.74-122845.4=$183082.96

If contracts doesn't get renewed(probability=.20), everything will be same except that plan will be sold after 1 year at 400000$

Then capital gain tax =( 400000- 500000×.75)×.35=$8750

After tax sale= 400000-8750=391250$

PV of this after tax sale= 391250/1.14=343201.75$

And depreciation tax is available only flin first year which is = 500000×.25×.35=43750

Its pv = 43750/1.14=38377

NAL= 441309.62-38377-37027.09-343201.74=22703.79

EXPECTED NAL = 183082.96×.80 +22703.79×.2= 151007$

In case of lease, there will be only one outflow which is lease rental of $75000 in advance i.e. on the beginning of the year and tax savings on the se at the end of the year for $75000×.35=26250$

If contracts renewed after one year

NAL= PV of lease= 75000((1-1.14^-5)/.14)×1.14 -26250(1-1.14^-5)/.14=$203410

If it doesn't get renewed plan will be sublet at rent 75000$ (why? Because it has to cover the operating cost of lease) ,assume that we will get this rent at the end of the year

So PV of this rent = after tax rent×(1-1.14^-5)/.14

=75000×(1-.35)×(1-1.14^-5)/.14=$167363

NAL in this case = PV of lease- PV of rent

= 203410-167363= 36047$

EXPECTED NAL= 203410×.8+36047×.2= 169937.4$

Since expected NAL or net cost is lower in buying and borrowing, company should go with that option.