Question

Riverton Mining plans to purchase or lease

$ 430 comma 000$430,000

worth of excavation equipment. If​ purchased, the equipment will be depreciated on a​ straight-line basis over five​ years, after which it will be worthless. If​ leased, the annual lease payments will be

$ 97 comma 133$97,133

per year for five years. Assume​ Riverton's borrowing cost is

7.0 %7.0%​,

its tax rate is

40 %40%​,

and the lease qualifies as a true tax lease.

a. If Riverton purchases the​ equipment, what is the amount of the​ lease-equivalent loan?

b. Is Riverton better off leasing the equipment or financing the purchase using the​ lease-equivalent loan?

c. What is the effective​ after-tax lease borrowing​ rate? How does this compare to​ Riverton's actual​ after-tax borrowing​ rate?

Answer 1

a. If Riverton purchases the​ equipment, what is the amount of the​ lease-equivalent loan?

For this we need to know the incremental cash flow of the option , over lease

If it is purchased the cashflows in Yr. 0 will be -430000 & annually, for 5 yrs. Depn. Tax shields of (430000/ 5 yrs.*40% tax rate )= $ 34400--ie. Savings in tax

If leased , annual cash outflows, for 5 yrs. will be 97133*(1-40%)= $ 58279.80

Now,lease Vs buy incremental cash flows will be:

Year	0	1	2	3	4	5
Lease		-58279.8	-58279.8	-58279.8	-58279.8	-58279.8
Buy	-430000	34400	34400	34400	34400	34400
Lease-Buy	430000	-92679.8	-92679.8	-92679.8	-92679.8	-92679.8

Now, amount of the​ lease-equivalent loan=PV of the above incremental cash flows (Yrs. 1 to 5)discounted at the after-tax borrowing cost, ie. 7%*(1-40%)= 4.20%

ie.92679.8*(1-1.042^-5)/0.042=

410286.08

b. From the above, it is evident that leasing the equipment is cheaper by 430000-410286= $ 19713.

NPV(19713) of incremental cash flows is POSITIVE.

So, Riverton will be better off leasing the equipment

c..

Effective​ after-tax lease borrowing​ rate is the IRR of the above incremental cash flows

2.55%

whereas,

Actual​ after-tax borrowing​ rate =7%*(1-40%)=4.2%