Name:

Econ 135: Corporate Finance

Midterm Exam 1 – Answer key

Multiple Choice Questions (12 points)

Circle the right answer. Each question is worth 2 points.

1) A loan where the borrower pays interest each period, and repays some or all of the principal of the
loan over time is called a(n) _________ loan.
A) amortized
B) continuous
C) balloon
D) pure discount
E) interest-only

2) A bond sold five weeks ago for $1,200. The bond is worth $1,040 in today's market. Assuming no
changes in risk, which of the following is FALSE?
A) The bond has less time to maturity today than it did five weeks ago.
B) The bond has a smaller premium today than it did five weeks ago.
C) Interest rates must be higher now than they were five weeks ago.
D) The bond's current yield has increased from five weeks ago.
E) The coupon payment of the bond must have increased.

3) A current asset is:

A) An item currently owned by the firm.
B) An item that the firm expects to own within the next year.
C) An item currently owned by the firm that will convert to cash within the next 12 months.
D) The amount of cash on hand the firm currently shows on its balance sheet.
E) The market value of all the items currently owned by the firm.

4) Interest earned on both the initial principal and the interest reinvested from prior periods is called:
A) free interest
B) annual interest
C) simple interest
D) interest on interest
E) compound interest

5) Which of these methods does NOT reduce conflicts of interest?

A) Separating the role of CEO and chairman
B) Paying executives with stocks
C) Paying executives with stock options
D) Paying interest to bond holders before paying any dividends to shareholders
E) Preventing external auditors from doing consulting work for the companies they audit

6) A stock's next expected dividend divided by the current stock price is the:
A) Current yield.
B) Total yield.
C) Dividend yield.
D) Capital gains yield.
E) Earnings yield.
 Numerical problems (30 points)

Please show all calculations. If you're stuck, assume a solution to get full credit on a later part.

1) (7 pts.) LimLop Inc.'s income statement and balance sheet are as follows:

Revenue 400 Assets Liabilities

COGS 300 Cash 100 Accounts payable 50
SG&A 50 Account receivable 150 Total current liabilities 70
EBIT 50 Inventory 150 Long-term debt 430
Interest 10 Total current assets 400 Paid-in capital 500
Taxes 10 Fixed assets 1300 Retained earnings 700
Net income 30 Total assets 1700 Total liabilities and 1700
equity

a) (2 pts.) If the firm has an average tax rate of 25%, what is the net income?
Taxable income = EBIT – interest = 50 – 10 = 40.
Taxes = taxable income * average tax rate = 40 * 25% = 10

b) (2 pts.) What is the firm's ROE?

ROE = NI / Total equity = 30/1200 = 2.5%

c) (3 pts.) What are the 3 components of the DuPont analysis, with specific values for this company?
PM = NI/sales = 30/400 = 7.5%
TAT = Sales/Total assets = 400/1700 = 23.5%
EM = Total assets/Total equity = 1700 / 1200 = 1.42

2) (9 pts.) Biogenetics, Inc. plans to retain and reinvest all of their earnings for the next 30 years. At the
end of year 31, the firm will begin to pay a $30 annual dividend, followed by a dividend of $31.20 at
the end of year 32. Dividends will grow at the same rate forever.

a) (2 pts.) What's the expected growth rate of dividends?

g = D32/D31 -1 = 31.20/30 – 1 = 4%

b) (2 pts.) Given a required return of 14%, what should the stock sell for in 30 years?
P30 = D31/(k-g) = $30 / (.14 - .04) = $300

c) (2 pts.) What should the stock sell for today?

P0 = $300 / 1.1430 = $5.89

d) (1 pt.) If the stock currently trades for $10, is it overvalued, undervalued, or fairly priced, and
why?
Since $10 > $5.89, the stock is currently overvalued.

e) (2 pts.) What's the dividend yield in year 30?

Dividend yield30 = D31/P30 = 30/300 = 10%
Name:

3) (4 pts.) LimLop Inc's bonds have a 6% coupon rate. The bonds have a maturity of 20 years. Similar
bonds have a YTM of 5%.

a) (2 pts.) What is the price of LimLop's bonds?

Price = $30/ .025 [(1 - 1/1.02540)] + 1,000 / 1.02540 = $753.08 + $372.43 = $1,125.51

b) (2 pts.) What's a good reason for a firm to raise money by issuing bonds instead of equity?
Since interest is tax deductible, while dividends are not, issuing bonds reduces the tax liability of
the firm.

4) (6 pts.) Suppose you buy a new Toyota for $25,000, paying nothing down. You agree to a repayment
schedule of equal monthly payments over six years, beginning one month from today. The banker's
required return is 10% APR.

a) (2 pts.) How much will your monthly payments be?

C = 25,000 (.10/12) / (1 - 1/(1+.10/12)72) = $463.15

b) (2 pts.) What is the outstanding balance on the loan after 24 months?

PV = 463.15/(.10/12) [1 – 1/(1+.10/12)48] = $18,261.15

c) (2 pts.) What is the effective annual rate on the loan?

EAR = (1+.10/12)12 – 1 = 10.47%

5) (4 pts.) Your spreadsheet looks like this:

A B C D E F G
1 Discount rate 20%
2 Year 0 1 2 3 4 5
3 Cash flow -100 -20 20 30 30 50
4 Discount factor
5 PV

a) (2 pts.) The discount factor is the number by which you multiply a FV to get its PV. What
formula should you enter into cell B4 to define the discount factor, so that you can copy and paste
that formula to all cells beside it, while being able to change the discount rate easily?
=1/(1+$B1)^B2 or =1/(1+$B$1)^B2 or =1/(1+$B1)^B$2 or =1/(1+$B$1)^B$2

b) (2 pts.) What formula should you enter into cell B5 to get the sum of PVs of all 6 cash flows?
=sumproduct(B3:G3,B4:G4) or =B3*B4+C3*C4+D3*D4+E3*E4+F3*F4+G3*G4
 Equation sheet Calculating returns and variability
Percentage return on stock: R = Dt+1/Pt + (Pt+1 – Pt)/Pt
Cash flow calculations
OCF = EBIT + depreciation – taxes Historical Expected
OCF = (sales-costs)(1-T) + depreciation*T (without 1 n n

interest) R = ∑ Ri E ( R ) = ∑ pi Ri
Net capital spending = Ending NFA – beginning NFA +
n i =1 i =1
n
n
depreciation 1 σ 2 = ∑ pi ( Ri − E ( R )) 2
Change in NWC = Ending NWC – beginning NWC
σ2 = ∑ ( Ri − R )2
n − 1 i =1 i =1
CFFA = OCF – net capital spending – change in NWC
σ = σ2
CF to creditors = interest paid – net new borrowing σ = σ2
CF to stockholders = dividends paid – net new equity
raised Portfolios
m
Some financial ratios E ( RPi ) = ∑ w j E ( Rij )
Current ratio = current assets / current liabilities j =1

Quick ratio = (current assets – inventory)/current n

liabilities E ( RP ) = ∑ pi E ( RPi )
Cash ratio = cash / current liabilities i =1

Total debt ratio = (total assets – total equity) / total n

assets σ 2 = ∑ pi ( E ( RPi ) − E ( RP )) 2
i =1
Debt-equity ratio = total debt / total equity
m
Times interest earned ratio = EBIT/interest
Cash coverage ratio = (EBIT + depreciation) / interest βP = ∑ wj β j
j =1
Inventory turnover = COGS / average inventory
Inventory period = 365 days / inventory turnover
A/R turnover = credit sales / average accounts receivable Capital market theory and the cost of capital
A/R period = 365 days / accounts receivable turnover E ( Ri ) − R f
A/P turnover = COGS / average accounts payable
SML : E ( RM ) − R f =
βi
A/P period = 365 days / accounts payable turnover
Operating cycle= inventory period + A/R period CAPM : E ( Ri ) = R f + β i ( E ( RM ) − R f )
Cash cycle = operating cycle – A/P period E P D
WACC = RE + RP + R D (1 − TC )
Other equations V V V
Value of financial leverage
ROA*b
Internal growth rate = PV of interest tax shield = Tc D
1− ROA*b
ROE *b CFFA
Sustainable growth rate = VU = if CFFA is constant forever
1− ROE *b R
" VL = VU + TC D
C 1 %
Annuity PV = $1− '
r # (1+ r)t &
C
Perpetuity PV =
r
After-tax salvage = salvage – TC*(salvage – book value)
Fisher effect: 1+r=(1+R)(1+h)

Stock valuation
P0=(D1+P1)/(1+k)
Constant dividends: P0=D/k
Dt (1+ g) Dt+1
Dividend growth model: Pt = =
k−g k−g