Quiz 2, Fin 350
Please use the following information to answer questions 1-5
A stock pays a level dividend of $4 per share every year forever. The discount rate is 10%.
1. What is the stock price at year 5?
(a) $30
(b) $40
(c) $50
(d) $60
(e) None of the above
(B)
P5= Div/r = 4/0.1=$40, since the dividends after year 5 forms a standard perpetuity and the
stock price at year 5 is the present value at year 5 of a standard perpetuity.
2. What is the stock price now (at year 0) if you plan to buy one share of stock and hold it for
two years?
(a) $60
(b) $50
(c) $40
(d) $30
(e) None of the above
(c)
P0= div/(1+r) +div/(1+r)^2 + P2/(1+r)^2, where P2 is the stock price at year 2.
P3 =div/r =4/0.1=$40.
P0= 4/1.1+4/1.1^2 + 40/1.1^2 =$40.
The basic idea in this question is that the stock price is the present value at year 0 of three
pieces of cash flows: two dividend payments and the stock price at year 2, since you will sell the
stock at year 2 if you don’t want to hold it.
In summary, for level dividends, the stock price at any year is the same, $40 in this specific
question.
3. What is the stock price now if you plane to buy one share and hold it for five years?
(a) $60
(b) $50
(c) $40
(d) $30
(e) None of the above
(c)
Similar to the problem above,
P0= div/(1+r) + div/(1+r)^2 + div/(1+r)^3 + div/(1+r)^4 + div/(1+r)^5 +P5/(1+r)^5
=$40, where div=$4, r=10% and P5= div/r =$40.
4. What is the dividend yield now?
(a) 0
(b) 10%
(c) 15%
(d) 5%
(e) None of the above
(b)
Dividend yield now = div1/P0 =4/40 =10%, since div1 =div =$4
5. What is the dividend yield at year 2?
(a) 0
(b) 10%
(c) 15%
(d) 5%
(e) None of the above
(b)
Dividend yield at year 2 = div 3 /p2 =4/40 = 10%, since div3 = div =$4, and P2=div/r =$40.
Please use the following information for questions 6 -12.
A stock is expected to have an earnings of $4 per share next year. The discount rate is 10%.
The return on equity is 15%.
6. If all the earnings are paid out as dividends, what is the stock price now ?
(a) $60
(b) $50
(c) $40
(d) $30
(e) None of the above
(c)
If there is no plow-back, all the earnings are paid out as dividends and dividends will form a
standard perpetuity with the level dividend of $4 every year. In this case, all the questions are
like the questions 1-5 above.
P0 =div/r =4/0.1 =$40, since the stock price at time zero is the present value at time zero of
future dividends, which are a standard perpetuity.
7. If all the earnings are paid out as dividends, what is the dividend at year 4 ?
(a) $6
(b) $5
(c) $4
(d) $3
(e) None of the above
(c)
Dividend at year 4 =$4, as discussed in question 6.
8. If all the earnings are paid out as dividends, what is the stock price at year 5 ?
(a) $60
(b) $50
(c) $40
(d) $30
(e) None of the above
(c)
P5 =div/r =4/0.1=$40, since the stock price at year 5 is the present value at year 5 of a
standard perpetuity.
9. If the manager wants to keep or plow back 20% of profit or earnings, then what is the stock
price now?
(a) $60
(b) $40
(c) $56
(d) $46
(e) None of the above
(d)
If there is a plow-back, then we have to use the dividend growth model to find out the stock
price at any year. It is very important to remember that if there is plow-back, there is a growth
of dividends and dividends are then a growing perpetuity ( not a standard perpetuity).
At year 0, P0 = div1/(r-g), where g = ROE * plow-back-ratio = 0.15 *0.2 =3%, div1 =earnings1 *
payout-ratio = 4*(1-0.2)=$3.2.
P0= 3.2/(0.1-0.03) =$46.
10. If the manager wants to keep or plow back 20% of profit or earnings, then what is the
dividend yield now?
(a) 0
(b) 10%
(c) 7%
(d) 3%
(e) None of the above
(c)
Dividend yield now (at year 0) = div1/P0 = 3.2/46 = 7%, where div1 and P0 are
calculated
In question 9.
11. If the manager wants to keep or plow back 20% of profit or earnings, then what is the PVGO
at year 1?
(a) $9
(b) $8
(c) $7
(d) $6
(e) None of the above
(C)
PVGO at year 1( the present value added at year one to each share due to plowing back
earnings to take good projects) = the stock price at year 1 with a plow-back – the stock price at
year 1 without a plow-back = 47 -40 =$7, where with the plow-back of 20%,
P1=Div2/(r-g)=3.2*1.03/(0.1-0.03) =$47.
12. If the manager wants to keep or plow back 20% of profit or earnings, then what is the
dividend at year 4?
(a)
(b)
(c)
(d)
(e)
$6.50
$5.50
$3.50
$4.50
None of the above
(c)
Div4 = div1*(1+g)^(4-1) =div1*(1+g)^3 =3.2*1.03^3 =$3.50, since g =3%, calculated in
question 9.
13. Given the following cash flows for project A: C0 = -$2,000, C1 = $1,000 , C2 = +$1,000 and
C3 = $1,000, calculate the payback period.
a)
b)
c)
d)
One year
2 years
3 years
None of the above
b) By definition of the payback period for a project.
14. The IRR is defined as:
A)The discount rate that makes the present value of future cash flows equal to the initial
(time zero) investment cost
B)The difference between the cost of capital and the present value of the cash flows
C)The discount rate used in the NPV method
D)The discount rate used in the discounted payback period method
E) None of the above
(A) The definition of IRR by setting NPV =0, which is the same as choice A.
15. Project A has the following cash flows: C0 = $100, C1 = -$120. The cost of capital for project
A is 10%, which of the following is correct?
A) Reject the project since the IRR is smaller than the cost of capital
B)Take the project since the IRR is larger than the cost of capital
C) Take the project since the NPV is negative
D) None of the above
(D) IRR =20% by the definition of IRR by setting NPV at zero. However, this is a borrowing
project. IRR =20% means the interest rate for borrowing this money is 20%, which is larger than
10%, the available interest rate in the market.
16. In the lecture, how many approaches are discussed to calculate the cash flows from
operations?
A) one
B) two
C) three
D) None of the above
(c)
17. The principal short-term assets are:
A) Cash
B) Accounts receivable
C) Inventories
D) All of the above
E) None of the above
(D)
18 . Proper treatment of inflation in the NPV calculation involves:
A) Discounting nominal cash flows using the nominal discount rate
B) Discounting real cash flows using the real discount rate
C) Discounting nominal cash flows using the real discount rates
D) A and B
E) None of the above
(D)
Use the following to answer questions 19-21.
A new project will generate sales of $50 million, costs of $25 million, and depreciation expense
of $5 million in the coming year. The firm’s tax rate is 50%.
19. What is the tax payment in the coming year?
A) $30 million
B) $20 million
C) $10 million
D) None of the above
The pre-tax profit = sales (rev) –cost –depreciation = 50-25-5 =$20 million
The tax = the pre-tax profit * tax rate =20*50% =$10 million.
C)
20. What is the net profit (or net income or accounting profit) in the coming year ?
A) $30 million
B) $20 million
C) $10 million
D) None of the above
C)
Net profit (earnings) =pre-tax profit –tax payment =20 -10 =$10 million
21. What is the cash flow from operations in the coming year?
A) $30 million
B) $20 million
C) $10 million
D) None of the above
D)
There are three approaches to calculate the cash flow from operations.
If we use the second approach,
the cash flow from operations = net profit (earnings) +depreciation =10 +5 =$15 million.
Using the first approach,
the cash flow from operations = sales (rev) – cost – tax payment =50 -25 -10 = $15 million
Using the third approach,
The cash flow from operations =(sales –cost)*(1-tax-rate)+depreciation * tax-rate
= (50-25)*(1-0.5) + 5*0.5 =$15 million.
A)