Describe the difference between discounting and interest, referring to the way we have talked about it...

Describe the difference between discounting and interest, referring to the way we have talked about it in class.
Specifically use this example: A company is looking to purchase an item worth 10k today. The same item can be purchased 3 years later for 10k. Why is the second option more desirable, and how much more desirable is it if your cost of capital is 5%?

Solutions

Expert Solution

Scenario 1 :

The Present Value(PV) of Item = 10000

Cost of Capital = 5%

Interest Charged in 3 years = 10000* 5%*3 = 1500

Scenario 2 :

Value of Item 3 years later = 10000

Value of this item discounted to present time = Future value(FV) of Amount * 1/(1+r)ⁿ

= 10000 * 1/(1+ 5%)³

= 8638.375985

So, the cost value of an item costing 10000 in future is actually 8638.375985 in present terms. Comparing this with an item costing 10000 in PV implies that the second option is more desirable as it will involve less cost incurrence.

The idea of determining/bringing the FV of an asset to the present value is called discounting. This helps us understand the current value of a future income/expense. In this question 10000 in FV is worth 8638.375985 in PV.

Therefore, discounting will bring down the PV of an item with a fixed FV

It is more desirable to the extent of money saved, i.e. PV option 1 – PV of Option 2 = 10000 - 8638.375985 = 1361.624015

Interest on the other hand is an added amount on the PV of good thus increasing it in the future. Therefore interest will push up the FV of an item with fixed PV.

Infact after 3 years, the 10000 of today will become 10000+ 1500 = 11500 in FV.

Rahul Sunny answered 1 month ago

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