Question

In: Finance

1. You expect to receive $4,400 upon your graduation and will invest your windfall at an...

1. You expect to receive $4,400 upon your graduation and will invest your windfall at an interest rate of 0.69 percent per quarter until the account is worth $5,725. How many years do you have to wait until you reach your target account value?

2.

McCann Co. has identified an investment project with the following cash flows.

Year. Cash Flow

1. $950

2. 1,050

3. 1,330

4. 1,160

a. If the discount rate is 8 percent, what is the present value of these cash flows?

b. What is the present value at 19 percent?

c. What is the present value at 26 percent?

Solutions

Expert Solution

1)

Given

present value = $4,400

future value = $5,725

interest rate = 0.69 % = 0.0069

Apply future value formula as below

future value = present value*(1+r)^t

Applying the value in above formula

$5,725= $4400*(1.0069)^t

$5,725/$4400= (1.0069)^t

$1.3011=(1.0069)^t

take ln both side we get**

ln (1.3011) = t × ln(1.0069)

0.263210061= t*0.00687630394

0.263210061/0.00687630394

t = 38.2778398 quarters

so time in years will be

time = 38.2778398/4 Years   

time = 9.569 years

** Note : x^n=y (use natural log calculator)

n=logy

     logx

=log1.3011

   log1.0069

=0.263210061

0.00687630394

=38.2778398

2)

Present Value=FV/(1+r)^n

​where:FV=Future Value

r=Rate of return

n=Number of periods​

similarly

Year Annual cash flows ($) Present Value Factor (PVF) at 8.00% Present Value of annual cash flows ($)
[Annual cash flow x PVF]
1 950 0.9259 879.605
2 1,050 0.8573 900.165
3 1,330 0.7938 1055.754
4 1,160 0.735 852.6
TOTAL 3688.124

The Present value of the cash flows will be $3688.124

B)

Year Annual cash flows ($) Present Value Factor (PVF) at 19.00% Present Value of annual cash flows ($)
[Annual cash flow x PVF]
1 950 0.8403 798.285
2 1,050 0.7062 741.51
3 1,330 0.5934 789.222
4 1,160 0.4987 578.492
TOTAL 2907.509

The Present value of the cash flows will be $2907.509

c)

Year Annual cash flows ($) Present Value Factor (PVF) at 26.00% Present Value of annual cash flows ($)
[Annual cash flow x PVF]
1 950 0.7937 754.015
2 1,050 0.6299 661.395
3 1,330 0.4999 664.867
4 1,160 0.3968 460.288
TOTAL 2540.565

The Present value of the cash flows will be $2540.565

jeff jeffy answered 2 years ago
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