topic 3 examples

8/10/2019 Topic 3 Examples

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Topic 3 Examples [1] TVM: Investment Valuation

Topic 3 In-Class ExamplesTVM Application: Investment Valuation

3.1 A project requires an initial investment of $50,000. The project will generate net cash flows of $15,000 at theend of the first year, $40,000 at the end of the second year, and $10,000 at the end of the third year. The

projects cost of capital is 13%. Calculate the projects NPV and IRR.

3.2 Project P requires an investment of 4,000 at time 0. The investment pays 2,000 at time 1 and 4,000 at time 2.Project Q requires an investment of X at time 2. The investment pays 2,000 at time 0 and 4,000 at time 1.

The net present values of the two projects are equal at an interest rate of 10%. Calculate X .

(A) 5,400(B) 5,420

(C) 5,440(D) 5,460(E) 5,480


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3.3 Mike receives cash flows of 100 today, 200 in one year, and 100 in two years. The present value of these cashflows is 364.46 at an annual effective rate of interest . Calculate .

(F) 10%(G) 11%(H) 12%

(I) 13%(J) 14%

3.4 A renter with $1,104 has a one year lease. The landlord is willing to accept two payment options:(i) $1,104 now; or(ii) $100 paid at the beginning of each month for twelve months.What monthly interest rate would be required for the two options to be equivalent?

(A) Less than 0.012(B) At least 0.012 but less than 0.013(C) At least 0.013 but less than 0.014(D) At least 0.014 but less than 0.015(E) At least 0.015

3.5 One annuity pays 5 at the end of each year for 40 years another annuity pays 6 at the end of each year for 20years. The present values of the two annuities are equal at an effective rate of interest i . Find i .


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3.7 You have decided to invest in Bond X, an n-year bond with semi-annual coupons and the followingcharacteristics: Par value is 1,000 The ratio of the semi-annual coupon rate to the desired semi-annual yield rate, is 1.03125 The present value of the redemption value is 381.50

Given = 0.5889 , what is the price of bond X?

(A) 9.50%(B) 9.75%(C) 10.00%(D) 10.25%(E) 10.50%

3.8 Bill buys a 10-year 1,000 par value 6% bond with semi-annual coupons. The price assumes a nominal yield of6%, compounded semi-annually. As Bill receives each coupon payment, he immediately puts the money intoan account earning interest at an annual effective rate of i .

At the end of 10 years, immediately after Bill receives the final coupon payment and the redemption value ofthe bond, Bill has earned an annual effective yield of 7% on his investment in the bond. Calculate i .

(A) 9.50%(B) 9.75%(C) 10.00%(D) 10.25%(E) 10.50%


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3.9 A $1,000 par value 10-year 8% bond has semi-annual coupons. The redemption value equals the par value.The bond is purchased at a premium to yield 6% convertible semi-annually. What is the amount foramortization of the premium in the tenth coupon?

(A) Less than $7.20(B) At least $7.20, but less than $7.25

(C) At least $7.25, but less than $7.30(D) At least $7.30, but less than $7.35(E) $7.35 or more

3.10 A 10-year bond with par value of $1,000 is purchased to yield 8% convertible semi-annually. Par value equalsto redemption value. The interest-paid portion of the first semi-annual coupon is $44.50. At what nominalrate of interest convertible semi-annually are the coupons paid?

(A) Less than 7.75%(B) At least 7.75%, but less than 8.50%

(C) At least 8.50%, but less than 9.25%(D) At least 9.25%, but less than 10.00%(E) 10.00% or more


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3.11 A 1,000 bond with semi-annual coupons at (2) = 6% matures at par on October 15, 2020. The bond ispurchased on June 28, 2005 to yield the investor (2) = 7% . What is the purchase price paid by a bond buyer?

(F) 906(G) 907(H) 908

(I) 919(J) 925

3.12 A $1,000 par value bond has 7.5% semi-annual coupons and matures on July 1, 2017 at $1,050. Find the actualselling price of this bond on November 15, 2013 and the price that would be quoted in a financial newspaperon the same date, based on a nominal annual yield rate of 5.80% compounded semi-annually. Use the actualnumber of days for the calculations.


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3.13 A 10-year callable bond pays semi-annual coupons at a rate of 6% per year. The bond is callable after 5 yearsat 102. The bond is priced to yield 7% compounded semi-annually. Determine the price of the callable bond.

3.14 A 10-year callable bond pays semi-annual coupons at a rate of 6% per year. The bond is callable after 5 yearsat 102. The bond is priced to yield 5% compounded semi-annually. Determine the price of the callable bond.

3.15 A 1,000 par value bond pays annual coupons of 80. The bond is redeemable at par in 30 years, but is callableany time from the end of the 10 th year at 1,050. Based on her desired yield rate, an investor calculates thefollowing potential purchase prices, : Assuming the bond is called at the end of 10 th year, = 957 Assuming the bond is held until maturity, = 897

The investor buys the bond at the highest price that guarantees she will receive at least her desired yield rateregardless of when the bond is called. The investor holds the bond for 20 years, after which time the bond iscalled. Calculate the annual yield rate the investor earns.

(A) 8.56%(B) 9.00%(C) 9.24%(D) 9.53%(E) 9.99%


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3.18 A common stock is purchased on January 1, 1992. It is expected to pay a dividend of 15 per share at the endof each year through December 31, 2001. Starting in 2002 dividends are expected to increase K % per yearindefinitely, K % < 8%. The theoretical price to yield an annual effective rate of 8% is 200.90. Calculate K .

(A) 0.86(B) 1.00

(C) 1.14(D) 1.28(E) 1.42

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