Determining Yield to Maturity Through the DCF Model
If we know the price of a bond, we can use the DCF model to determine the yield to maturity of the bond. We do this by taking the price of the bond as the initial payment. In our calculation, this payment will be negative, because it is an outflow of cash. We then determine the present value of all the cash flows and solve for the discount rate when the net present value is set to 0. This discount rate is the internal rate of return. The IRR is equal to the bond’s yield to maturity. If we solve for the discount rate, it comes out to 6.2%. Thus, the yield to maturity on this bond is 6.2%. Solving for the IRR is impossible to do with a simple calculator, so you won’t be required to do this on the exam, but it is still important to understand how the IRR (which is equivalent to its YTM) is calculated.
|
|
Cash Flows |
Net Present Value Formula |
|
Initial Payment |
– $950 |
-$950 + |
|
Year #1 Payment |
+ $50 |
$50 / (1 + rate) + |
|
Year #2 Payment |
+ $50 |
$50 / (1 + rate)2 + |
|
Year #3 Payment |
+ $50 |
$50 / (1 + rate)3 + |
|
Year #4 Payment |
+ $50 |
$50 / (1 + rate)4 + |
|
Year #5 Payment |
+ $50 |
$50 / (1 + rate)5 + |
|
Year #5 Payment |
+ $1,000 |
$1,000 / (1 +rate)5 = |
|
Sum |
$250 |