Question

5. ​The Cable Chemical Corporation is considering the purchase of a chemical analysis machine. Although the machine being considered will result in an increase in revenue of $150,000 and cash expenses of $65,000 per year, it has a purchase price of $450,000, and it would cost an additional $50,000 to correctly install this machine. In addition, to properly operate this machine, inventory must be increased by $30,000. This machine has an expected life of 10 years, after which it can be sold for $50,000. This machine is being depreciated down to zero. There is a 30% tax rate, and a required rate of return of 15%.

Required:

a) Determine whether or not Cable Chemical should purchase the machine.

b) Assume that you are considering the purchase of a 20-year, bond with an annual coupon rate of 10%. The bond has a par value of $1,000, and it makes annual interest payments. If you require an 8% yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? Explain why the price is different from the par value.

Answer 1

a)

Initial cash outflow = purchase price + installation + increase in inventory

= 450,000 + 50,000 + 30,000

= 530,000

Depreciation = 500,000 / 10 = 50,000

Yearly cash flow = (increase in revenue - increase in cash expenses)*(1-tax) + depreciation* tax rate

= (150,000 - 65,000)*(1-30%) + 50,000*30%

= 59,500 + 15,000

= 74,500

Terminal cash flow = after tax salvage value + recovery of working capital

After tax salvage value = 50,000*(1-30%) = 35,000

Terminal cash flow = 35,000 + 30,000 = 65,000

Present value of future cash flows =

74500*PVIFA(r = 15% ; n = 10) + 65000*PVF(r=15% ; n=10)

= 389,965.27

NPV = Present value of future cash flows - initial cash outflow

= 389,965.27 - 530,000

= -$140,034.73

Since NPV is negative machine should not be purchased

b)

Price of a bond is present value of future cash flows discounted at YTM

Coupon = 1000*10% = 100

Rate = 8%

Number of periods = 20

Price = 100*PVIFA(r = 8% ; n =10)+1000*PVF(r =8% ; n=20)

Maximum price = $1196.36

the price is different from par value because YTM and coupon rate both are not equal

when YTM < Coupon rate,bond trades at premium.