BFW 2631FINANCIAL MANAGEMENT

TUTORIAL SET 2 –WEEK 2 SOLUTIONSFINANCIAL MATHEMATICS

Important note to students: It is your responsibility to familiarize yourself with your own personal calculator. Teaching staff are familiar with the Sharp EL735 and Sharp EL738 Business Financial Calculator. Assistance will be provided with the Sharp EL735/EL738 calculator in teaching materials. If you are using any other model then you must learn how to use them yourself. Do not leave learning the calculator until the last minute. You are also required to attempt all tutorial questions on your own prior to attending class. Question One At 6 percent interest, how long does it take to

a. double your money? b. quadruple it?

Solution

(a) Using the 72 Rule the time to double an investment at an interest rate of 6% is approximately = 72/6=12 years

0 i=6% 12 i=6% 24 (b)

X 2X 4X

So it should take approximately 24 years for an investment to quadruple at an interest rate of 6%

Alternatively

(a) 2X= X(1+i)n n=

ln (2)ln (1 . 06 )

=11.8956 =12 years

(b) 4X= 2X(1+i)n n=

ln (2)ln (1 . 06 )

=11.8956 =12 years

Total time taken for X to amount to 4X is approximately 24 years

Question Twoa. You are offered an investment that requires you to put up $3,000 today in exchange for

$10,000 in 15 years from now. What is the annual rate of return on this investment?b. A bank offers you an interest of 8%, compounded quarterly. Which investment will you

choose (take the investment opportunity in part (a) or invest at this bank)?Solution

2(a) Annual rate of return = i=[ FVPV ]

1/n

−1= [ $10 ,000$3 ,000 ]

(1/15 )

−1 =0.0836 or 8.36%

Clear the memory before any operation [2ndF] then [ALPHA] then [0] then [0]

Values Function Keys Display on Calculator Screen15 [N]

8.363000 [±] [PV]10000 [FV]

[COMP] [I/y]

2(b) Effective Annual Rate = [1+ 0 .08

4 ]4

−1=8 .24 %

Choose the Investment in part (a) since the Annual Rate of return of 8.36% from the investment in part (a) > Bank’s EAR =8.24%

Question ThreeAn investor deposits $10,000. Ten years later it is worth $17,910. What rate of return did the investor earn on the investment?Solution: $17,910 = $10,000 x (1+i)10

(1+i)10 = $17,910/10,000 = 1.7910 (1+i) = (1.7910) 1/10 = 1.060 i = .060 = 6.0% Using Calculator PV=$10000 FV=$17910 N=10 COMP [I/Y] DISPLAY 6

Question 4Today your stock is worth $50,000. You invested $5,000 in the stock 18 years ago. What average annual rate of return [i] did you earn on your investment?Solution: $50,000 = $5,000 x (1+i)18

(1+i)18 = $50,000/$5,000 = 10 (1+i) = (10) 1/18 = 1.135 i = 0.13646 or 13.65% Using Calculator PV=$5000 FV=$50000 N=18 COMP [I/Y] DISPLAY 13.65%

Question FiveSuppose you make an investment of $1,000. The first year, the investment returns 12%, the second year it returns 6%, and the third year it returns 8%. How much would this investment be worth, assuming no withdrawals are made?Solution 0 YR1 1 YR2 2 YR3 3 I=12% i=6% i=8%

10001.12 x (1.06) x (1.08) =$1,282

Question SixAs a financial manager, you have to decide whether or not to undertake a project, which involves an initial cost or cash outflow of $1,000 and yields the following expected cash inflows.

a. Illustrate the cash flows as they arise on a time line. b. What is the implied rate of return on this project? c. If your company’s cost of funds is 8%, would you undertake the project based on the net present value of the above cash flows? Solution6(a) 0 1 2 3

-$1000 $300 $600 $900

6(b) Using Calculator

1000± [ENT], 300[ENT], 600[ENT], 900[ENT], [2ndF] [CFi] [COMP]i=29.728%

6(c) 0 1 2 3

($1,000) $300 $600 $900

277.78 =

$300(1 .08 )

514.40 =

$ 600

(1 .08 )2

714.45=

$ 900

(1 .08 )3

End of Year Cash Flow($)1 3002 6003 900

$506.63 > 0

Alternatively Using the Sharp EL735/EL738 Business / Financial CalculatorClear the memory before any operation [2ndF] then [ALPHA] then [0] then [0]

Time Period Cash Flow Function Keys Display on Calculator Screen0

$1000 [± ] [ENT]

DATA SET: CF0.00

1 $300 [ENT] DATA SET: CF1.00

2 $600 [ENT] DATA SET: CF2.00

3 $900 [ENT] DATA SET: CF3.00

[2ndF] [CFi] RATE(I/Y)=0.00

8 [ENT] RATE(I/Y)=8.00

[▼] NET_PV=0.00

[COMP] 506.63

Since NPV =$506.63 > 0 The project adds value to the firm and hence is worth undertaking.