Using the data in Exhibit 1, Betta begins his credit risk assessment by calculating the maximum price an investor is willing to currently pay for a Bay Corp bond when considering credit risk. He assumes continuous compounding and that US government bonds are risk free.
EXHIBIT 1
BOND DATA FOR BAY CORPORATION
| Par value | $5,000,000 |
| Maturity | 4.0 years |
| Risk-free rate; zero-coupon yields | 1.25% |
| Bay Corp credit spread | 0.75% |
| Bond type | Zero coupon |
Q. Based on the data in Exhibit 1, Betta’s calculation would show that the maximum price an investor is willing to pay for Bay Corp bonds is closest to:
- $4,615,580.
- $4,852,228.
- $4,619,227.
Solution
A is correct. The promise to pay $5,000,000 in four years is worth $4,615,582 when considering the time value of money (risk-free rate) and credit risk (credit spread) using continuous compounding. The calculation is as follows:
| Total yield | = | 1.25% + 0.75% |
| = | 2.00% |
| Discount factor | = | 1(e0.02×4)1e0.02×4 |
| = | 0.923116 |
$5,000,000×0.923116 = 4,615,580
此题我对2%取了ln，然后用连续复利公式算出来正好是C，然后答案没有对2%进行处理，是不是该取ln求连续复利的折现率？
