Question

company of $20,000 is to be received 10 years hence, followed by a $40,000 payment 17 years from the present. If over this time span the annual inflation rate is 5% while the expected annual market rate is 9%, calculate the present equivalent these two payment using

a. Actual – dollar analysis

b. Constant – dollar analysis

Answer 1

Following information is given

• Amount of $20,000 will be received at end of 10 years
• Amount of 40,000 will be received at end of 17 years
• The inflation rate is 5% or r=5%
• The annual market rate is 9% or i=9%

To calculate the present value as per Actual –dollar analysis

The formula will be

Pw = first cash inflow / (1+i)ⁿ + Second cash inflow / (1+i)ⁿ

Where

Pw = present value

First cash flow = $20,000

i=9% or 0.09

n= the year at which cash inflow was received

Putting the value

Pw = $20,000 /(1+0.09)¹⁰ + $40,000 / (1+0.09)¹⁷

= $20,000 / (1.09)¹⁰ + $40,000/(1.09)¹⁷

= $20,000/ 2.367364 +$40,000/ 4.327633

= $8448.216 +$ 9242.927

=$ 17691.14

The present value will be $17691.17 as per actual dollar analysis

B

To calculate the present value as per Constant – dollar analysis

The formula is

Pw(i^’,r) = first cash inflow / (1+ i^’)ⁿ (1+r)ⁿ + second cash inflow / (1+ i^’)ⁿ (1+r)ⁿ

Where

I^’= (1+i)/(1+r) – 1

Where

i=9% or 0.09

r=5% or0.05

putting values

= (1+0.09)/(1+0.05) -1

=(1.09 /1.05) -1

=1.03809 -1

= 0.03809

Putting the values in the formula

Pw(i^’,r) = first cash inflow / (1+ i^’)ⁿ (1+r)ⁿ + second cash inflow / (1+ i^’)ⁿ (1+r)ⁿ

= $20,000/ (1+0.03809)¹⁰(1+0.05)¹⁰ + $40,000 /(1+0.03809)¹⁷(1+0.05)¹⁷

= $20,000 /(1.03809)¹⁰(1.05)¹⁰ +$40,000 /1.03809)¹⁷(1.05)¹⁷

=$20,000 /(1.453283)( 1.628895) +$40,000 /(1.88797)( 2.292018)

=($20,000/ 2.367244) +($40,000/4.327262)

=$8448.642 +$9243.72

=$17692.36

The present value is $17692.36

There is no major difference between the values