Download Solution for the first exam:

Solution for the first exam:
Part B:
1. Give two reasons why the corporate may prefer debts, such as bank loans and
bonds, to equities when it comes to financing its new project. Give one reason
why the financial investor (householders or those with surplus funds) prefer bonds
or bank deposits / loans to equities.
Main Points:
Two reasons why the corporate prefers debts to equities:
1) Interest payment for debts are tax-deductible expense, but dividends of
equities are not;
2) Equities open up a chance for hostile take over.
One reason why the financial investor prefers bonds or bank loans to equities:
equities have the most severe problem of information asymmetry (or
principal-agent problem and adverse selection).
2. By utilizing the Dupont System for the ratio analysis, show that an index of
short-run profitability can easily be exaggerated at the expense of the long-term
financial stability of the company.
Dupont System= Net Profit / Shareholder’s equities = (Net Profit / Total
Sales)*(Total Sales / Total Asset)*(Total Asset / Shareholder’s equities) = Return
On Equities
It is very hard for the company to control the first two components because profit
and sales are not under control. However, if a company wants to make the ROE
looks great, it would borrow money to buy back its equities. As the equities
decreasing, the ROE would increase because net profit, total sales and total asset
are same. The problem is that the rate of loans is high and it is higher possibility to
be bankruptcy in the long run.
Part C: (Tips: before write calculate, remember to write down all relevant formulas. In
next exam, all students should present the formula with symbols first; otherwise, no
mark would be given.)
1. Suppose that you are borrowing funds from a bank. The bank is quoting “10%),
“interest rate calculated semi annually.”
1) What is the effective annual interest rate for you if you pay the interest rate (along
with the part of the principal sum of the loan)?
2) What is the effective monthly interest rate for you if you pay the interest every
month?
Answer:
Formula:
r
effective
=( 1+ i / m )m/f -1
( i = quoting rate from the bank; m= how many times calculated yearly by the bank;
f= how many times pay the interest yearly)
1)
r
effective annual
2)
r
effectivemonthly
=(1+ 0.1 / 2)2/1 -1 =1.052 -1 = 0.1025 = 10.25%;
= (1+ 0.1 / 2)2/12 -1 =1.051/6 – 1 =1.0082 – 1 = 0.0082 = 0.82%;
2. You are 30 years old, and have just started working. You are making a retirement
plan for your future. You wish to retire at the age of 60, and live 20 years
afterwards. You wish to save enough, say $X, at the end of each year while you
are working so that from the deposit, you will have an annuity due payment of
$50,000 per annum( at the beginning of the year) for the living expense of your
post-retirement life. Your spouse may live 5 more years, and you wish to make an
annual allowance of $20,000 for the remaining life span of your widowed spouse
(to be paid at the beginning of each year as well). The effective interest rate is
assumed to be constant at 5% throughout the entire time span.
1) Take the time point of your retirement (age 30) as the present. Show the formula
for the sum of the time values of the deposits you have made up to that point of
time (from the age of 30 to the age of 60). What would be the sum of the time
values (at the time of your retirement) of the two annuity dues (which will take
place over time after your retirement)? How much you will have to save at the end
of each year while you are working in order to have the above annuity dues?
Solve for $X.
2) Take the time point of now (age 30) as the present. Show the formula for the
present value of your annuity deposit while you are working. What is the present
value of your annuity dues of your post retirement life (including the allowance
for your widowed spouse)? Solve for the annual depsit for $X.
Answer
1) Time point:
age 30
age 60
PV
age 80
5 more yrs
Annuity:
Annuity Dues:
n
FV = A{[ (1+r) – 1] / r}
FV = A{[ (1+r)n – 1] / r}(1+r)
PV = A{[1- 1/(1+r)n]/r}
PV = A{[1- 1/(1+r)n]/r}(1+r)
Now, we set age 60 as the time point of Present Value, so, to age 30, the Present Value
of age 60 is the Future Value. Therefore, we get the formulas:
FV to age30 =X{[ (1+0.05)30 – 1] / 0.05}=X[(4.322-1) / 0.05] = 66.439X
PVatage60=50,000{[1-1/(1+0.05)20]/0.05}(1+0.05)+20,000{[1-1/(1+0.05)5]/0
20
.05}(1+0.05)[1/(1+0.05) ]
= 50,000* [(1-0.3769) / 0.05]*1.05 +
20,000*[(1-0.784) / 0.05]*1.05-29 = 654,266 + 34,260 = $ 688,526 (they got
paid at the beginning of each year, so, use Annuity Dues formula)
FV to age30 = PVat age60
X= 688,526 / 66.439 = $10,363
2) Time point
age 30
PV
age 60
age 80
5 more yrs
Now, age 30 is the time point of present value. ‘You’ need to know how much must
save every year between age 30 to age 60 to get annually $50,000 within twenty years
after age 30, and to give $20,000 yearly to ‘your’ widowed wife. The amount of
money is X.
We can get the formula:
PVat age30 = X*{[1- 1 / (1+0.05)30 ] / 0.05}= X* [(1-0.2314) / 0.05] = 15.372X
We can get another formula to know how much present value of $50,000 and $20,000
at age 30.
PV’at age30 = 50,000 {[1-- 1 / (1+0.05)20 ] / 0.05}*1.05*(1 / 1.0530) + 20,000*{[1-- 1 /
(1+0.05)5 ] / 0.05}*1.05*(1 / 1.0550) = 50,000 * 3.028 + 20,000 * 0.396 =151,000 +
7,919 = $158,919
PVat age30 = PV’at age30
X = 158,919 / 15.372 = 10,364
3. Suppose that you are evaluating a proposed investment project in Canada. The
initial investment requires the immediate payment of $100,000 for the purchase of the
machine and equipment. The project will take two full years ( for preparation at no
further costs than initial payment for the equipment and machine ) until it starts
bringing the revenues. Once it starts, the project will bring the after tax net profits of
$40,000 per annum at the end of each year for the peri9od of 6 years. The corporate
income tax rate is 40%, and the capital cost allowance (depreciation) rate is 30% per
annum. The Canadian tax authority allows you to write only half of the depreciation
off in the first year.
1) Suppose that the ‘quoted’ nominal interest rate your bank charge for the funding
of this project is 10% per annum. The bank calculates the interest rate twice a year,
and the interest is paid once a year. Suppose that there is no sale of the expired
project equipment or machine: in other words, there is no ‘salvage’.
 what would be the effective annual interest rate charged by the bank?
 What is the Net Present Value of this investment project, which includes the
tax shields or tax savings due to the government’s capital cost allowances?
2) Suppose that the above investment is going to be funded with your money. If your
money is invested elsewhere, say in the bond market, it can bring in the annual
rate of return of 6%. Should you invest your money on this project or elsewhere?
Evaluate it on the basis of the method of Internal Rate of Return (you do not have
to calculate it; simply show the formula and explain the steps).
3) Suppose that the machine and equipment of this investment project will be sold at
$20,000 at the end of the life span (when the investment ceases to be productive).
What would be the Net Present Value of this project? – No need for the
calculation for the final line of answer.
Answer:
1) Formula of Net Present Value:
NPV = -C + R(1-T)*{[1-1 / (1+k)n] / k}+ [CdT / (d+k)]*[(1+0.5k) / (1+k)]
First, need to get the effective annual interest rate:
k
effective annual
=( 1+ i / m )m/f -1 = (1+0.10 / 2) 2/1 -1 = 0.1025
Put k=0.1025, C = $100,000, R=$40,000 (after-tax revenue), d =0.3, T =0.4, and
n=6 years into the NPV formula. Also, because it took two years to prepare the
project until it brings the revenues. Therefore, we can get:
NPV = - 100,000 + 40,000*{[1-1 / (1+0.1025)6] / 0.1025}* [1 / (1+0.1025)2]
+[ 100,000*0.3*0.4 / (0.1025 + 0.3)]* [ (1+0.5*0.1025) / (1+0.1025)] = -100,000
+ 40,000 * 4.3235 * *0.8227 + 28,235*0.9535 = -100,000 + 142,279 +28,427 =
70,706
2) The value of k while makes the NPV equal to zero is the Internal Rate of Return.
Based on the above, we can get:
0 = - 100,000 + 40,000*{[1-1 / (1+k)6] / k}* [1 / (1+ k)2] +[ 100,000*0.3*0.4 / (k
+ 0.3)]* [ (1+0.5*k) / (1+k)]
And then calculate the formula and get k or IRR while the formula is equal to
zero.
If k is larger than 6%, this means the investment on the project could generate
more revenue than on the bond market, so keeping continuing the project;
If k is smaller than 6%, the bonk market is a better choice than the project, and
stop the project.
.
3) The only difference between 1) and 3) is that the machine and equipment could be
sold at $20,000 at the end of the life span. That is, the Salvage Value or Sn
=$20,000.
The formula would be:
NPV = -C + R(1-T)*{[1-1 / (1+k)n] / k}+ [CdT / (d+k)]*[(1+0.5k) / (1+k)] - SndT
/ [(d+k)(1+k)n] + Sn / (1+k)n
NPV = - 100,000 + 40,000*{[1-1 / (1+0.1025)6] / 0.1025}* [1 / (1+0.1025)2]
+[ 100,000*0.3*0.4 / (0.1025 + 0.3)]* [ (1+0.5*0.1025) / (1+0.1025)] +
(20,000*0.3*0.4) / [(0.3+0.1025)(1+0.1025)8] + 20,000 / (1+0.1025)8 = -100,000
+ 142,279 +28,427 – 2,732 + 9,162= 77,136