(5) Graph: You have been asked by your boss to evaluate three mutually exclusive
ID: 2730266 • Letter: #
Question
(5) Graph: 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
(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?
(d) (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.
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
Explanation / Answer
a.
r = m × [ ( 1 + i)1/m - 1 ]
Where,
i = Effective Rate per period = 14%
m = 365 days
t = 1 year
r = 13.1052%
b.
r = ei - 1
Where:
r = effective interest rate
i = nominal annual interest rate = 14%
e = 2.71828183
r = 15.027%
c.
FV = PV*e^(rt)
where r is the continuously compounded interest or discount rate which is different from the discrete compounded or discount rate.
FV = 10*e^(0.10)
= 10*1.1052
= $11.052
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