Name (please print)
Sal U. Shunn
ENG 106 – Engineering Economics
Final
Winter 2011
You may use eight sheets of hand-written notes. No other reference materials, calculators or other electronic
devices are allowed. State any assumptions, show all your work and explain where appropriate. You may use
shorthand notation, e.g., (P/A, 5%, 3), where helpful. Do not use Excel functions unless asked to do so.
The test has six problems and 100 points.
1. (20 pts) Dewittrite Industries plans to invest $3 million in projects this year. To generate the necessary capital,
the corporation plans to borrow $0.8 million from a bank at a before-tax interest rate of 7%/yr, sell bonds worth
$1.2 million, and retain $1 million in after-tax earnings. The bonds will cost Dewittrite 9%/yr (before tax), and the
corporation’s stockholders expect an 11%/yr rate of return on their investment. Dewittrite’s marginal income tax
rate is 43%, and the general inflation rate is 3%/yr.
Set up all the relationships
needed to determine Dewittrite’s
weighted after-tax cost of capital in %/yr.
Could set this up as a table:
Source
B.T. cost, %/yr
A.T. cost, %/yr
Fraction of
total capital
Fraction*A.T. cost, %/yr
Loan
7%
7%*(1-43%)
$0.8/$3
(0.8/3)* 7%*(1-43%)
Bonds
9%
9%*(1-43%)
$1.2/$3
(1.2/3)* 9%*(1-43%)
Retained Earnings
11%
$1/$3
(1/3)* 11%
Sums:
$3/$3
Weighted A.T. cost
of capital, %/yr
Or as a more compact relationship:
Weighted A.T. cost, %/yr ={[(loan cost, %/yr)*loan $ + (bond cost, %/yr)*bond $](1- marginal tax rate)
+ (equity cost, %/yr)*retained earning $}/total $ of new capital
={[(7%/yr)*$0.8 million + (9%/yr)*$1.2 million](1- 0.43) + (11%/yr)*$1 million}/$3 million
2. (10 pts) Grace & Katherine & Associates have been asked by the IRS to develop a new MACRS depreciation
schedule (for tax purposes) by using the following assumptions: eight-year depreciation period, 150% declining
balance method with conversion to straight-line, zero salvage value, and half-year convention. Set up the
relationship(s)
needed to determine the depreciation ($) in the first tax year for an asset with a cost basis of $W.
If use 150% DB to begin:
D1, $ = (1/2)(1.5/8)($W)
Any DB method over 100% will be greater than SL in the first year, but if this is not obvious, could also
check for immediate conversion to SL:
D1, $ = (1/2)($W - $0)/8
The 150%DB depreciation is larger, so use it in the first tax year.