Question

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?

Answer 1

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