Question

You have inherited $1.6 million from your old uncle. What is the present value of this cash flow if you receive it at the following times?

1. Suppose the right discount rate from the market is 3%.

(a) Now.

(b) In 5 years.

(c) In 10 years.

(d) In 50 years.

2. Suppose the discount rate now rises to 8%.

(a) Now.

(b) In 5 years.

(c) In 10 years.

(d) In 50 years.

Answer 1

We know that present value equation is given by the following,

Present value = CFt/ (1+r)^t

Where,

CF = Cash flow in t years

r = discount rate

t = time period in years

1. a) If you receive the cash flow now

CF0 = 1.6 Million = 16,00,000

r = 3% = 0.03

t = 0

Substituting the given values in the above equation we get,

Present value = 16,00,000/ (1+0.03)^0

Present value = 16,00,000/ 1

Present value = 16,00,000 = 1.6 million

1. b) If you receive the cash flow in 5 years

CF5 = 1.6 Million = 16,00,000

r = 3% = 0.03

t = 5

Substituting the given values in the above equation we get,

Present value = 16,00,000/ (1+0.03)^5

Present value = 16,00,000/ (1.03)^5

Present value = 16,00,000/ 1.1593

Present value = 13,80,174.06 or 1.38 million

1. c) If you receive the cash flow in 10 years

CF10 = 1.6 Million = 16,00,000

r = 3% = 0.03

t = 10

Substituting the given values in the above equation we get,

Present value = 16,00,000/ (1+0.03)^10

Present value = 16,00,000/ (1.03)^10

Present value = 16,00,000/ 1.3439

Present value = 11,90,550.26 or 1.19 million

1. d) If you receive the cash flow in 50 years

CF50 = 1.6 Million = 16,00,000

r = 3% = 0.03

t = 50

Substituting the given values in the above equation we get,

Present value = 16,00,000/ (1+0.03)^50

Present value = 16,00,000/ (1.03)^50

Present value = 16,00,000/ 4.3839

Present value = 3,64,971.33 or 0.36 million

2.a) If you receive the cash flow now

CF0 = 1.6 Million = 16,00,000

r = 8% = 0.08

t = 0

Substituting the given values in the above equation we get,

Present value = 16,00,000/ (1+0.08)^0

Present value = 16,00,000/ 1

Present value = 16,00,000 = 1.6 million

2. b) If you receive the cash flow in 5 years

CF5 = 1.6 Million = 16,00,000

r = 8% = 0.08

t = 5

Substituting the given values in the above equation we get,

Present value = 16,00,000/ (1+0.08)^5

Present value = 16,00,000/ (1.08)^5

Present value = 16,00,000/ 1.4693

Present value = 10,88,933.12 or 1.09 million

2. c) If you receive the cash flow in 10 years

CF10 = 1.6 Million = 16,00,000

r = 8% = 0.03

t = 10

Substituting the given values in the above equation we get,

Present value = 16,00,000/ (1+0.08)^10

Present value = 16,00,000/ (1.08)^10

Present value = 16,00,000/ 2.1589

Present value = 7,41,109.58 or 0.74 million

2.d)If you receive the cash flow in 50 years

CF50 = 1.6 Million = 16,00,000

r = 3% = 0.08

t = 50

Substituting the given values in the above equation we get,

Present value = 16,00,000/ (1+0.08)^50

Present value = 16,00,000/ (1.08)^50

Present value = 16,00,000/ 46.9016

Present value = 34,113.97 or 0.03 million

Therefore,

if the discount rate is 3%

Time period	Present value of 1.6 million
Now	1.60 million
in 5 years	1.38 million
in 10 years	1.19 million
in 50 years	0.36 million

if the discount rate is 8%

Time period	Present value of 1.6 million
Now	1.60 million
in 5 years	1.09 million
in 10 years	0.74 million
in 50 years	0.03 million