17)
Shin Satellite Corp. issues 10,000 debenture bonds with a face value of $26,000 each and a
bond interest rate of 18% per year payable semiannually. The bonds have a maturity date
of 10 years. If the market interest rate is 14% per year, compounded semiannually, what is
the present worth of one bond to a person who wants to purchase it and earn the market
rate?
17)
Answer:
$31,508.36
Explanation:
From VN=C(P/F, i%, N) +rZ(P/A, i%, N)
Where i=0.14/2 =700 or 7.00%
r= (18%)/2= (9%)
N =20
Thus, present worth of the bond
=26,000 (P/F, 7%, 20) +2340 (P/A, 7%, 20)
=6718.40 +24,789.96
=31,508.36
18)
The cost of building the gondola lift system that transports visitors from the tops of the
mountain peaks to the valley at the Zhangjiajie National Forest Park in China is $10.5
million. The lift system will need an annual maintenance cost of $164,000, and the
elevators will need to be replaced every 5 years with the estimated cost of $603,000, for an
indefinite period of time. What is the capitalized worth of the lift system at an interest rate
of 16% per year?
18)
Answer:
–$12,072,976.25
Explanation:
CW (16%) = – 10,500,000 –164,000/0.16 –603,000 [(A/F, 16%, 5)]/0.16
= – 10,500,000 –1,025,000.00 –603,000 (0.1454)/0.16
= – 12,072,976.25
19)
A 24–hour music network plans to add satellite technology to allow its expansion into
other major southern markets. The network expects the monthly revenue to increase by
$380,000 from new cable subscription fees. The satellite will require an initial cost of $2
million with monthly operating and maintenance costs of $340,000. It will have a $122,000
salvage value after 6 years. Calculate the net present worth of this investment at an
interest rate of 4% per year, compounded continuously.
19)
Answer:
$655,389.00
Explanation:
The nominal interest per month is 0.33%.
PW = – 2,000,000 + 40,000 (P/A, 0.33%, 72) +122,000 (P/F, 0.33%, 72)
= – 2,000,000 + 40,000 (63.9798) +122,000 (0.7885)
=655,389.00
20)
Boilermaker Brew Plc. and Hoosier Brewing Co. plan to combine their U.S. operations in
an attempt to bolster their sagging sales in a tough domestic market. The two companies
will form a new unit called HoosierMaker. The companies expect to invest $120 million
upfront to set up the new unit. HoosierMaker expects to garner revenue of $9.5 million
each year and spend $1.3 million a year in costs, over the next 7 years. What is the future
worth of this investment if the companies‘ rate of return is 16% per year?
20)
Answer:
–$245,550,020.00
Explanation:
FW = – 120,000,000 (F/P, 16%, 7) –1,300,000 (F/A, 16%, 7) +9,500,000 (F/A, 16%,
7)
= – 120,000,000 (2.8262) +8,200,000 (11.4139)
= – 245,550,020.00
7
21)
Aztec Corp., a clothing retailer, plans to open another 95 stores by the end of the year.
Each new store will require an initial investment of $270,000 and an annual operating cost
of $24,000. Each will have a $61,000 salvage value after 5 years. The company expects to
garner revenue of $36,000 each year. What is the future worth of this investment if the
company‘s minimum attractive rate of return is 13% per year, compounded semiannually?
21)
Answer:
FW for each store is –$367,349.00.
Explanation:
Effective interest rate =(1 +r/M)M– 1 =(1+0.13/2)2–1
=0.1342 or 13.42%
For Each store,
FW = – 270,000 (F/P, 13.42%, 5) –24,000 (F/A, 13.42%, 5) +36,000 (F/A, 13.42%, 5)
+61,000
= – 270,000 (1.8769) + 12,000 (6.5345) +61,000
= – 367,349.00
22)
AmeriTextile Co. is considering opening a production and shipping facility in Dallas to
keep up with demand for its pillows. The 105,000–square–foot facility will require an
initial investment of $280,000, and an annual operating cost of $26,000. It will have a
$74,500 salvage value after 9 years. Calculate the net present worth of this investment if
the company’s minimum attractive rate of return is 5% per year.
22)
Answer:
–$416,780.10
Explanation:
PW = – 280,000 –26,000 (P/A, 5%, 9) +74,500 (P/F, 5%, 9)
= – 280,000 –26,000 (7.1078) +74,500 (0.6446)
= – 416,780.10
23)
Quinn purchases a bond for $29,000 when the market interest rate is 13% per year,
compounded semiannually. The bond has an interest rate of 10% per year payable
semiannually and a maturity date of 24 years. What is the face value of this bond?
23)
Answer:
$37,155.91
Explanation:
From VN=C(P/F, i%, N) +rZ(P/A, i%, N), we need to find C ( Z = C).
Where i=(1 +r/M)M– 1 =0.13/2 =0.065 or 6.50%
r= (10%)/2= (0.05%)
N =48
Thus, 29,000 = C (P/F, 6.5%, 48) +0.05C (P/A, 6.5%, 48)
C = (29,000)/ [(P/F, 6.5%, 48) +0.05(P/A, 6.5%, 48)]
=29,000/ [0.0487 +0.05(14.6359)]
=37,155.91
8
24)
Determine the internal rate of return of the following cash flow.
Year Cash Flow, $ Year Cash Flow, $
0–450,000 656,000
150,000 757,000
252,000 858,000
353,000 959,000
454,000 10 60,000
555,000 11 61,000
24)
Answer:
5.41%
Explanation:
PW = 0 = – 450,000 +50,000 (P/A, i*%, 11) + [2000 (P/A, i*%, 10) + 1000 (P/G, i*%,
10)]
(P/F, i*%, 1)
Solve for i by interpolation.
PW(5%) = – 450,000 +50,000 (P/A, 5%, 11) + [2000 (P/A, 5%, 10) + 1000 (P/G, 5%,
10)]
(P/F, 5%, 1)
=10,173.58
PW(6%) = – 450,000 +50,000 (P/A, 6%, 11) + [2000 (P/A, 6%, 10) + 1000 (P/G, 6%,
10)]
(P/F, 6%, 1)
= – 8562.86
25)
Consider the following cash flow. Determine the annual worth if the minimum attractive
rate of return is 9% per year.
Year Cash Flow, $ Year Cash Flow, $
0–150,000 615,000
113,000 715,400
213,400 815,800
313,800 916,200
414,200 10–14 16,600
514,600 15 17,000
25)
Answer:
–$3656.81
Explanation:
AW = – 150,000 (A/P, 9%, 15) +13,000 +400 (P/G, 9%,10)(A/P, 9%, 15)
+ [3600 (F/A, 9%, 5) +400] (A/F, 9%, 15)
= – 150,000 (0.1241) +13,000 +400 (24.3728)(0.1241) + [3600 (5.9847) +400] (
0.0341)
= – 18,615.00 +13,000 +1209.87 +748.32
= – 3656.81
9
26)
Dean bought a $26,000 bond that has interest rate of 8% per year payable semiannually, 3
years ago. The bond has a maturity date of 12 years from the date it was issued. How
much should he be able to sell the bond for today, if the current market interest rate is 9%
per year, compounded semiannually?
26)
Answer:
$24,419.20
Explanation:
From VN=C(P/F, i%, N) +rZ(P/A, i%, N)
Where i=(1 +r/M)M– 1 =0.09/2
=0.045 or 4.50%
r= (8%)/2= (4%)
N =18 periods remaining in the life of the bond.
Thus, present worth of the bond
=26,000 (P/F, 4.5%, 18) +1040 (P/A, 4.5%, 18)
=11,772.80 +12,646.40
=24,419.20
27)
Sony Corporation has invested $5.6 million in developing super–thin TVs based on new,
organic light–emitting diode technology. The company plans to market the OLED TVs in
an 11–inch size and produce 24,000 units for the first five years. The annual production
and operating cost is estimated at $350 per unit and will be sold at $400 per unit.
Determine the internal rate of return for this investment if the study period is five years.
27)
Answer:
2.34%
Explanation:
PW = 0 = – 5,600,000 + (50) (24,000) (P/A, i%, 5)
Solve for i by interpolation.
PW(2%) = – 5,600,000 + (1,200,000) (P/A, 2%, 5) =56,151.41
PW(3%) = – 5,600,000 + (1,200,000) (P/A, 3%, 5) = – 104,351.38
28)
Thai Savings Bank issues 100,000 bonds as a response to the Thai Central Bank’s initiatives
to increase domestic saving. The bonds have a face value of $40,000 each, a bond interest
rate of 8% per year payable annually, and a maturity date of 14 years. What is the current
price of a bond, if the market interest rate is 9% per year, compounded semiannually?
28)
Answer:
$36,305.76
Explanation:
From VN=C(P/F, i%, N) +rZ(P/A, i%, N)
Where i=(1 +r/M)M– 1 =(1 +0.09/(2))2– 1
=0.0920 or 9.20%
r= (8%)/1= (8%)
N =14
Thus, present worth of the bond
=40,000 (P/F, 9.20%, 14) +3200 (P/A, 9.20%, 14)
=40,000 (0.2917) +3200 (7.6993)
=36,305.76
10
29)
Miner’s Mexican Grill Inc. plans to open its 100th restaurant by the end of next year. The
new restaurant will require an initial investment of $300,000 and an annual operating cost
of $31,000. It will have a $62,000 salvage value after 6 years. The company also estimates
that the new restaurant will bring in revenue of $43,400 each year. Determine the
acceptability of the investment if the company’s minimum attractive rate of return is 13%
per year using annual worth analysis.
29)
Answer:
The annual worth of –$55,207.60 is less than zero; therefore, the investment should
be rejected.
Explanation:
AW = – 300,000 (A/P, 13%, 6) –31,000 +43,400 +62,000 (A/F, 13%, 6)
= – 300,000 (0.2502) –31,000 +43,400 +62,000 (0.1202)
= – 55,207.60
The annual worth is less than zero; therefore, the investment should be rejected.
30)
The Bank of Tokyo–Mitsubishi issues 100,000 bonds as part of its liquidity and interest risk
management instrument. The bonds have a face value of $36,000 each, a bond interest rate
of 12% per year payable semiannually, and a maturity date of 16 years. The current price
of the bond is $69,662. Write the correct equation to determine if this bond should be
purchased using the IRR method, assuming an investor has a MARR of 4% per year,
compounded quarterly.
30)
Answer:
PW =69,662 =36,000 (P/F, i*%, 32) +2160 (P/A, i*%, 32)
Explanation:
From VN=C (P/F, i%, N) +rZ (P/A, i%, N)
r= (12%)/2= (6%)
N =32
The price of the bond equals the present worth of the bond.
PW =69,662 =36,000 (P/F, i*%, 32) + (0.06) (36,000) (P/A, i*%, 32)
=36,000 (P/F, i*%, 32) +2160 (P/A, i*%, 32)
If [(1 + i*)2– 1] (1 +0.04/4)4– 1, the bond should be purchased.
11
Answer Key
Testname: C5
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