Cost savings = 50,000/year
3year MACRs Depreciation
Required return = 10%
Tax Rate = 40%
What are the cash flow consequences of selling the old machine today instead of in 5 years?
Working
Pro Forma Income Statements
Year
1
2
3
4
5
Cost Savings
$50,000
$50,000
$50,000
$50,000
$50,000
Depreciation
New
Old
49,550
(9,000)
67,500
(9,000)
22,500
(9,000)
10,500
(9,000)
0
(9,000)
Incremental
$40,500
$58,500
$13,500
$1,500
$(9,000)
EBIT
Taxes (0.4)
$9,500
3,800
$(8,500)
(3,400)
$36,500
14,600
$48,500
19,400
$59,000
23,600
Net Income
$5,700
$(5,100)
$21,900
$29,100
$35,400
OCF
$46,200
$53,400
$35,400
$30,600
$26,400
Incremental Net Capital Spending
Year 0:
Cost of New Machine = $150,000 (Outflow)
Aftertax Salvage on Old Machine = $65,000
–
0.4 (65,000
–
55,000) = $61,000 (Inflow)
Incremental Net Capital Spending = $150,000
–
61,000 = $89,000
Year 5:
Aftertax Salvage on Old Machine = 10,000
–
0.4 (10,000
–
10,000)
= 10,000 (Outflow because we no longer receive this)
Year
0
1
2
3
4
5
OCF
$46,200
$53,400
$35,400
$30,600
$26,400
NCS
$(89,000)
(10,000)
Change in NWC






Total Project
Cash Flow
$(89,000)
$46,200
$53,400
$35,400
$30,600
$16,400
NPV = $54,812.10
IRR = 36.28%
20
Chapter 7: Interest Rates and Bond Valuation
Bond Definitions
Coupon
The stated interest payment made on a bond.
Face Value / Par Value
The principal amount of a bond that is repaid at the end of the term.
Coupon Rate
The annual coupon divided by the face value of a bond.
Maturity
The specified date on which the principal amount of a bond is paid.
Yield to Maturity (YTM)
The rate required in the market on a bond.
Bond Value = PV of Coupons + PV of Face Amount =
? × (
1−
1
(1+𝑟)
𝑡
𝑟
) +
?
(1+𝑟)
𝑡
Relationship between Coupon Rate and YTM
YTM = Coupon Rate
=>
Par Value = Bond Value
YTM > Coupon Rate
=>
Par Value > Bond Value (Discount Bond)
YTM < Coupon Rate
=>
Par Value < Bond Value (Premium Bond)
Current Yield vs. Yield to Maturity
Current Yield = Annual Coupon / Price
YTM = Current Yield + Capital Gain Yield
E.g. 10% coupon bond with semiannual coupons, face value of 1,000, 20 years to maturity, $1197.93
Current Yield = $100 / $1197.93 = 8.35%
Price in one year, assuming no change in YTM = $1193.68
Capital Gain Yield = $(1193.68
–
1197.93) / 1197.93 =  0.35%
YTM = 8.35%  0.35% = 8%
21
Interest Rate Risk
Interest Rate Risk
–
Changes in bond prices due to fluctuating interest rates.
All other things being equal,
Time to Maturity: The longer the time to maturity, the greater the interest rate risk.
o
Longerterm
bonds have greater interest rate sensitivity because a large portion of a bond’s value
comes from the face value.
o
Present value of this amount isn’t greatly affected by a small change in interest rates if the amount
is to be received in one year.
o
On the other hand, even a small change in interest rate, once compounded for several years, can
have significant effects on the present value.
Coupon Rate: The lower the coupon rate, the greater the interest rate risk.
o
If two bonds with different coupon rates have the same maturity, then the value of the one with the
lower coupon is proportionately more dependent on the face amount to be received at maturity.
o
Bond with higher coupon has larger cash flows early in its life, so its value is less sensitive to
changes in the discount rate.