# Expected return?

I understand the math, but can someone conceptually explain why a higher discount rate/expected return decreases value?

thanks

A higher discount rate (or _ required _ return) reduces the value. If you expect that an investment will return \$5 in one year, and you require a 10% annual return, the value (to you) is \$50. If you require a 12.5% annual return, the value (to you) is only \$40.

A higher _ expected _ return increases the value. If you expect a return of \$5 in one year and you require a 10% annual return, the value (to you) is \$50. If you expect a return of \$6, the value (to you) is \$60.

You’re welcome.

Maybe a got expected vs required mixed up. But why conceptually (in words) would a higher required return decrease value?

Opportunity cost.

Generally, a higher required return arises because the investment is riskier. The riskier the investment, the less you’re willing to pay (for a given expected return (amount)).

Theoretically, the value of ANY financial decision or claim should be the present value of the expected future cash flows. Conceptually, you can think of the PV as the amount that, if deposited today at the reguired rate of return in an account, would allow you to EXACTLY replicate the future cash flows. Let’s look at an example:

Assume a security paid you three cash flows - \$100 in one year, \$200 in 2 years, and \$300 in 3 years. Assume also that you require a 10% rate of return. The present value of these cash flows at 10% is 482.97. Verify for yourself (i.e. make a little spreadsheet) that if you put the \$482.97 into an account that earned 10% and took out \$100 at the end of year 1, \$200 at the end of year 2 and \$300 at the end of year 3, you’d have exactly nothing left after the third withdrawal. To get you started, in the first year, you’d earn \$48.30 in interest fpr a balance of 531.27, and after withdrawing the first payment, you’d then have \$431.27 remaining. Then do the same for the next two years and payments.

In other words, that \$482.97 (the present value of the cash flows) is WITH INTEREST exactly enough to duplicate the future cash flows. Since it replicates the cash flows it must have the same value as the cash flows.

Now calculate the PV at a 20% required rate – it’s now \$395.83. And if you deposited this amount in an account at 20% annual interest, you could then exactly duplicate the cash flows.

So why does the higer required rate (20% vs 10%) result in a lower PV (or price or value in this case)? Simple - In order to duplicate the cash flows in the second case, you earn more interest, so you need less to start with. Therefore, the value of the necessary amount needed to replicate the future cash flows is less, and so must the value be.

Thank you all for the help!