Question

Write out the formula and calculate the present value of the following sequence of willingness to pay

amounts: this year, $75; next year, $100; year 2, $150; year 3, $50. Use a 5 percent discount rate. Recalculate

using a discount rate of 10 percent. What is the effect of using a higher discount rate? Do individual people

value consumption today over consumption tomorrow? What about society? Should they/it? Why or why

not?

can anyone explain this to me? how to come up with the formula?

Answer 1

ANSWER:

When i = 5%

pv = amount in year 0 + amount in year 1(p/f,i,n) + amount in year 2(p/f,i,n) + amount in year 3(p/f,i,n)

pv = 75 + 100(p/f,5%,1) + 150(p/f,5%,2) + 50(p/f,5%,3)

pv = 75 + 100 * 0.9524 + 150 * 0.907 + 50 * 0.8638

pv = 75 + 95.24 + 136.05 + 43.19

pv = 349.48

when i = 10%

pv = amount in year 0 + amount in year 1(p/f,i,n) + amount in year 2(p/f,i,n) + amount in year 3(p/f,i,n)

pv = 75 + 100(p/f,10%,1) + 150(p/f,10%,2) + 50(p/f,10%,3)

pv = 75 + 100 * 0.9091 + 150 * 0.8264 + 50 * 0.7513

pv = 75 + 90.91 + 123.96 + 37.565

pv = 327.435

when discount rate is more present value decreases as when discount rate is 5% the pv is $349.48 while at 10% it is $327.435

Individual people will value consumption today more then tomorrow as they don't have anyone to take care of from tomorrow so they will borrow at a higher discount rate while as a society the consumption is valued tomorrow more valuable rather then today as society has to think about the future generations and so they will borrow at a lower discount rate.