Question

1) Your company intends to finance the purchase of a new construction crane. The cost is $1,500,000. Compare the interest cost of three different types of loans for 10 years (discount loan, interest only loan, amortized loan) at the interest rate of 8%.

Answer 1

Option 1) Discount only loan

Here Interest rate = 8% , Cost of crane = $1500,000 , n = 10 years

FV = PV(1+r)^n
=1500000(1+8%)^10
=1500000(1+0.08)^10
=1500000(1.08)^10
=1500000(2.158925)
=32,38,387.50$
Interest = 32,38,387.50 $ - 15,00,000 $
= 17,38,387.50 $

Option 2) Interest only loan

Interest = Principal x interest rate x 10 years

= 1500,000 x 8% x 10

= 12,00,000 $

Option 3) Amortized loan

Installment = Cost/PVIFA(r%,n)

PVIFA(r%,n) = [1-1/(1+r)^n / r ]

r= 8%, n = 10

PVIFA(8%,10)=[1-1/(1+8%)^10 / 8%]
=[1-1/(1.08)^10 / 0.08]
=[1-0.4632 / 0.08]
=[0.5368 / 0.08]
= 6.7101
=Installment = 1500000/6.7101
= 2,23,544.233 $
Thus Total payment made = 223544.23 x 10
= 2235442.33$
Thus total Interest payment = 2235442.33-1500000
=7,35,442.33 $

Thus it's better to take amortized loan