Question

4.

Please walk me through this problem. Step by step thoroughly. Also explain the equations used. also an explanation of how you came to the answer. Thanks i will love you if you do this.

You have been asked by your boss to evaluate three mutually exclusive projects. The cash flow estimates and costs of each project are given below:

	T=0	1	2	3	4	5	6	7
Project A	-3790	200	600	300	1000	2800
Project B	-3790	1000	1000	1000	1000	1000
Project C	-3790	0	0	0	0	0	0	5400

            (all numbers are in thousands of dollars)

As precisely as you can, describe how the most preferred project is related to the cost of capital.

(a) What rate, when continuously compounded, will yield a 14% annual rate?

(b) What is the effective annual rate when the 14% rate is continuously compounded?

(c)     Consider a cash flow of $10 every period in perpetuity starting one period from now (period t=0). What would be its price under continuous compounding of a 10% annual rate?

Answer 1

		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=cost of capital
		N=Year of Cash Flow
		As cost of capital changes,the PV chnges , consequently Net Present Value changes.
		The project with highest Net Present Value(NPV)is the most preferred project
		For example:
		If Cost of capitalis 5%=0.08
	N	Year	0	1	2	3	4	5	6	7
	A	Cash flow of project A	-3790	200	600	300	1000	2800			SUM
	PVa=A/(1.05^N)	PV of Cash Flow of Project A	-3790	190.4762	514.4033	238.1497	735.0299	1905.633	0	0	-206.308
	B	Cash flow of project B	-3790	1000	1000	1000	1000	1000			SUM
	PVb=B/(1.05^N)	PV of Cash Flow of Project B	-3790	952.381	857.3388	793.8322	735.0299	680.5832	0	0	229.1651
	C	Cash flow of project C	-3790	0	0	0	0	0	0	5400	SUM
	PVc=C/(1.05^N)	PV of Cash Flow of Project C	-3790	0	0	0	0	0	0	3837.679	47.67918
		Net Present Value of Project A	-206.308
		Net Present Value of Project B	229.1651
		Net Present Value of Project C	47.67918
		Most Preferred project	PROJECT B		(a) Annual Rate 0.14 r=Continuously compounded rate Future value of $1 after one year at continuously compounded rate of r=e^r Future value of $1 after one year at 14% aannualrate of (1+0.14) e^r=1.14 Ln 1.14=r (Ln=Natural Log) r= 0.131028 r=Continuously compounded rate 13.10% (b) Effective Rate when 14% rate is continuously Compunded: Future value of $1 at 14% continuously compounded rate=e^0.14= 1.150274 Future value of $1 at effective annualrate of I =(1+i) 1+i=1.150274 Effective Rate =i= 0.150274 Effective Rate 15.03% .(c) Effective annual rate when 10% rate is continously componded=(e^0.1)-1 Effective annual rate =(e^0.1)-1= 0.105171 Effective annual rate = 10.5171% Present Value of $10 per year in perpetuity $95.08 (10/0.105171)