Question

Question Nine

Mr West decides to deposit $5000 in a BankEast Ltd account that pays 8% p.a. continuously compounded. What will be his account balance in five years?

Question Ten

Norton Industries Pty Ltd is looking at investing in Project X that is expected to generate the following cash flows each year for six years.

Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
	$1 million	$1.5 million	$2 million	$2.5 million	$3 million	$3.5 million

Suppose similar investments are paying a return of 10% pa compounded semi-annually. How much should the Project X cost Norton Industries?

Please show works, don't use excel.

Answer 1

9.We need to use the future value for continuous compounding of the initial amount formula as follows:

ie. FV=P*e^(n*r)

where , FV=Future Value or balance in the a/c at end of 5 yrs.

P=the Principal, --- $ 5000

e--is the mathematical constant, 2.71828

n= no.of years--- here 5

r---rate of interest -- 8% p.a

Plugging the values , in the formula, we get the

FV=5000*2.71828^(5*0.08)=

7459.12

(Answer)

10.Cost of project X to Norton Industries=the sum of the Present values of the cash in-flows of the 6 yrs.

ie. PV=(CF1/(1+r)^1)+(CF2/(1+r)^2)+(CF3/(1+r)^3)+CF4/(1+r)^4)+CF5/(1+r)^5)+CF6/(1+r)^6)

Now plugging-in the given values for CFs & semi-annual r= 10%/2 ;n=no.of semi-annual compounding periods:

ie.PV=(1/(1+0.05)^2)+(1.5/(1+0.05)^4)+(2/(1+0.05)^6)+(2.5/(1+0.05)^8)+(3/(1+0.05)^10)+(3.5/(1+0.05)^12)=

Solving the above, in an online equation solver, we get the PV of the investment as

9.116283

millions

OR
Using PV Factors:
Year	CF in mlns	PV F at 5%		PV at 5%
1	2	3	4	5=2*4
1	1	1/1.05^2=	0.907029	0.907029
2	1.5	1/1.05^4=	0.822702	1.234054
3	2	1/1.05^6=	0.746215	1.492431
4	2.5	1/1.05^8=	0.676839	1.692098
5	3	1/1.05^10=	0.613913	1.841740
6	3.5	1/1.05^12=	0.556837	1.948931
				9.116283
Cost of the investment =PV= $ 9.116283 millions