Question

Please explain step by step.

ST Trucking just signed a contract. The contract calls for a payment of $1.1 million one year from today, $1.3 million two years from today, and $1.4 million three years from today. What is this contract worth today at a discount rate of 8.7 percent?

Answer 1

This question belongs to concept of 'Time value of Money'. so as we know that 1$ is not equal to 1$ today after 1 year Reason is that if this 1$ is kept in bank today at lets say 10% rightarrow they you can easily get $1.1 after a year. Also the inflation affects the purchasing power of people rightarrow so obvious an item worth 1$ today will cost more after an year. Now, applying some concept in this Question lets draw a timeline of cash payments first: Now if we simply Add all payments, it wont reflect the true worth because as we have seen above that $1.1 million is not $ 1.1 million Therefore we need to calculate present values of payments. \r\n Understand from this Diagram: Contract's Worth today = cash payment 1/(1 + r)^1 + cash payment 2/(1 + r)^2 + cash payment 3/(1 + r)^3 = $1.1 million/(1.087)^1 + $1.3 million/(1.087)^2 + $1.4 million/(1.087)^3 = [$ 1.1 million times 0.91996320147] + [$1.3 million times 0.846332292] + [$1.4 million times 0.778594565] = [$1.01195952 mill] + [$1.1002319796 mill] + [$1.090032 million] = $3.20222389 million ie 3202223.89 uparrow uparrow in millions in $