Managerial Economics Numerical's and Solutions
CHAPTER 1
THE
NATURE AND SCOPE OF MANAGERIAL ECONOMICS
1.
A firm is expected to earn $100,000 per
year forever. If the annual discount rate is 10percent, what is the present
value of the firm?
Solution:
The
present value interest factor for a perpetual annuity is 1/i, so the
value of the firm inthis case is 100,000/0.10 = $1,000,000
2.
A firm is expected to earn a profit of $10,000 per month for the next two years
and thento be sold for $1,000,000. If the discount rate is 1 percent per month,
what is the presentvalue of the firm?
Solution:
PV = 10,000 PVIFA0.01,24 + 1,000,000 PVIF0.01,24
PV = (10,000)(21.2434) + (1,000,000)(0.7876) =
1,000,034
3.
The owner of a firm has decided that he wants to sell it for $5,000,000, and he
sets out toincrease annual profits up to the level required to attain this
value. If the annual discountrate is 10 percent and the level of profit can be
expected to continue indefinitely, howmuch annual profit must the firm earn to
attain the value that the owner seeks?
Solution:
The
present value interest factor for a perpetual annuity is 1/i, so the
value of the firm inthis case is equal to profit times 1/0.10. Solving for
profit yields:
Profit
= (Value)(i) = (5,000,000)(0.10) = $500,000
4.
Phil is considering the purchase of a 10-year lease that will allow him to
operate aconcession stand at a local sports stadium. If the lease will cost
$100,000 and the relevantdiscount rate is 15 percent, what is the minimum
annual profit necessary to justify thepurchase?
Solution:
Value
= (Profit)(PVIFA0.15,10) so Profit = (Value)/(PVIFA0.15,10)
Profit
= (100,000)/(5.0188) = $19,925.08
5.
A firm is expected to earn $10,000, $25,000, $48,000, and $75,000 during the
next fouryears, after which it will be dissolved. What is the present value of
the firm if thediscount rate is 8 percent?
Solution:
PV = 10,000 PVIF0.08,1 +
25,000 PVIF0.08,2 + 48,000 PVIF0.08,3 +
75,000 PVIF0.08,4
PV = (10,000)(0.9259) + (25,000)(0.8573) +
(48,000)(0.7938) + (75,000)(0.7350)
PV = $123,918.90
6.
Fred is considering the purchase of a lease that will allow him to operate a
restaurant atthe local airport for a period of five years. The lease will cost
$33,522. Fred anticipatesannual profits of $10,000. At what discount rate will
Fred be indifferent betweenpurchasing and not purchasing the lease; that is,
what is the implied annual rate of returnon the cost of the lease?
Solution:
PV = (Profit)(PVIFAi,5)
so PVIFi,5 = (PV)/(Profit) = 33,522/10,000
= 3.3522
This
value of the PVIFA corresponds to a discount rate of 15 percent.
7.
Jane has compiled the following list of expenses after completing one year of
college.Assume that Jane would be living with her parents and working if she
weren't attendingcollege. Use this information to calculate Jane's economic
cost of attending college forone year.
Tuition
$ 8,000
Dormitory
room 4,000
Books
and supplies 1,000
Food
plan 3,000
Forgone
income 19,000
Entertainment
expenses 1,000
Clothing
2,000
Health
insurance 1,000
Solution:
Economic
cost = 8,000 + 4,000 +1,000 + 3,000 + 19,000 = $35,000
8.
Before Sarah quit her job as a carpenter, she was earning $35,000 per year. She
rented abuilding for $12,000 per year and opened a cabinet shop. She spends
$148,000 per yearfor labor, materials, utilities, and advertising.
(i)
How much revenue will the business have to earn in order to break even in
termsof business profit?
(ii)
How much revenue will the business have to earn in order to break even in
economic
terms?
(iii)
Suppose that Sarah buys the building. Now how much will the business have
toearn in order to break even in economic terms?
Solution:
(i)
Accounting cost = 12,000 + 148,000 = $160,000
(ii)
Economic cost = 35,000 + 12,000 + 148,000 = $195,000
(iii)
Economic cost remains the same. Accounting cost falls by $12,000.
9.
Vincent quit his $180,000-a-year job as an investment analyst to move to Tahiti
and paintsunsets and other natural vistas. The gallery that displays and sells
his paintings providesall of the canvas, paint, and other supplies he needs
without charge. If Vincent produces12 paintings per year, how much must he get
for one on average in order to yield aneconomic profit of zero?
Solution:
Economic
cost = 180,000/12 = $15,000
10.
Violet purchased a tract of land for $100,000. She quit her $30,000-a-year job
as a postalemployee and opened a skeet shooting range on her land. The range
generates $30,000 innet revenue after all day-to-day expenses have been
covered. Assume that the relevantdiscount rate is 10 percent. What is Violet's
business profit? What is her economic profit?
Solution:
Business
profit is $30,000.
Economic
cost = 30,000 + (0.10)(100,000) = $40,000, so she has an economic loss
of$10,000.
11.
A firm is expected to earn a profit of $60,000 per year forever. If the annual
discount rateis 8 percent, what is the present value of the firm?
Solution:
The
present value interest factor for a perpetual annuity is 1/i, so the
value of the firm inthis case is 60,000/0.08 = $1,125,000.
12.
A firm is expected to earn a profit of $20,000 per month for the next two years
and thento be sold for $1,000,000. If the discount rate is 1 percent per month,
what is the presentvalue of the firm?
Solution:
PV = 20,000 PVIFA0.01,24 +
1,000,000 PVIF0.01,24
PV = (20,000)(21.2434) + (1,000,000)(.7876) =
1,212,468
13.
The owner of a firm has decided that she wants to sell it for $4,000,000 and
she sets outto increase annual profits up to the level required to attain this
value. If the annualdiscount rate is 10 percent and the level of profit can be
expected to continue indefinitely,how much annual profit must the firm earn to
attain the value that the owner seeks?
Solution:
The
present value interest factor for a perpetual annuity is 1/i, so the
value of the firm inthis case is equal to profit times 1/0.10. Solving for
profit yields:
Profit
= (Value)(i) = (4,000,000)(0.10) = $400,000
14.
Joan is considering the purchase of a 10-year lease that will allow her to
operate aconcession stand at a local airport. If the lease will cost $150,000
and the relevantdiscount rate is 15 percent, what is the minimum annual profit
(to the nearest dollar)necessary to justify the purchase?
Solution:
Value
= (Profit)(PVIFA0.15,10) so Profit = (Value)/(PVIFA0.15,10)
Profit
= (150,000)/(5.0188) = $29,888
15.
A firm is expected to earn $5,000, $10,000, $20,000, and $30,000 during the
next fourears, after which it will be dissolved. What is the present value of
the firm if the discount rate is 8 percent?
Solution:
PV = 5,000 PVIF0.08,1 +
10,000 PVIF0.08,2 + 20,000 PVIF0.08,3 +
30,000 PVIF0.08,4
PV = (5,000)(0.9259) + (10,000)(0.8573) +
(20,000)(0.7938) + (30,000)(0.7350)
PV = $51,128.50
16.
Frieda is considering the purchase of a lease that will allow her to operate a
restaurant atthe local airport for a period of five years. The lease will cost
$37,908. Frieda anticipatesannual profits of $10,000. At what discount rate
will Frieda be indifferent betweenpurchasing and not purchasing the lease; that
is, what is the implied annual rate of returnon the cost of the lease?
Solution:
PV = (Profit)(PVIFAi,5)
so PVIFi,5 = (PV)/(Profit) = 37,908/10,000
= 3.7908
This
value of the PVIFA corresponds to a discount rate of 10 percent.
17.
Jim has compiled the following list of expenses after completing one year of
college.Assume that Jim would be living with his parents and working if he
weren't attendingcollege. Use this information to calculate Jim's economic cost
of attending college forone year.
Tuition
$ 10,000
Dormitory
room 6,000
Books
and supplies 1,000
Food
plan 4,000
Forgone
income 22,000
Entertainment
expenses 3,000
Clothing
1,000
Health
insurance 2,000
Solution:
Economic
cost = 10,000 + 6,000 +1,000 + 4,000 + 22,000 = $43,000
18.
Before Sam quit his job as a hairdresser, he was earning $34,000 per year. He
rented anoffice for $18,000 per year and opened a framing shop. He spends
$88,000 per year forlabor, materials, utilities, and advertising.
(i)
How much revenue will the business have to earn in order to break even in
termsof business profit?
(ii)
How much revenue will the business have to earn in order to break even in
economic
terms?
(iii)
Suppose that Sam buys the building. How will this influence the amount that
thebusiness will have to earn in order to break even in economic terms?
Inaccounting terms?
Solution:
(i)
Accounting cost = 18,000 + 88,000 = $106,000
(ii)
Economic cost = 34,000 + 18,000 + 88,000 = $140,000
(iii)
Economic cost will remain the same, assuming that the rental expense is equal
tothe opportunity cost of the building. Accounting cost will fall by $18,000
less anyadjustment for depreciation.
19.
Victoria quit her $80,000-a-year job as an artist to move to Los Angeles and
work as aninvestment consultant. The gallery that displayed and sold her
paintings provided all ofthe canvas, paint, and other supplies she needed without
charge. If Victoria finds 10clients per year, how much must she get paid by
each one on average in order to earn aneconomic profit of zero?
Solution:
Economic
cost = 80,000/10 = $8,000
20.
Vincent purchased 12 acres of land for $150,000. He quit his $40,000-a-year job
as apostal employee and opened a stable for boarding horses on his land. The
stable generates$50,000 in annual net revenue after all day-to-day expenses
have been covered. Assumethat the relevant discount rate is 10 percent. What is
Vincent's business profit? What ishis economic profit?
Solution:
Business
profit is $50,000.
Economic
cost = 40,000 + (0.10)(150,000) = $55,000, so he has an economic loss of$5,000.