so I need to use 400m discounting to market value to use DEAR formula??

More, I have one question in Q9 part d). I had to find other similar questions to study but it does not match my concept.

9. Bank Alpha has an inventory of AAA-rated, 15-year zero-coupon bonds with a face value of $400 million. The bonds currently are yielding 9.5% in the over-the-counter market. a. What is the modified duration of these bonds? MD=D/(1+R) = 15/(1.095) = 13.6986. b. What is the price volatility if the potential adverse move in yields is 25 basis points? 10-1 Price volatility = (MD) x (potential adverse move in yield) = (13.6986) x (.0025) = 0.03425 or 3.425 percent. c. What is the DEAR? why we can't use 400m (face value)? Daily earnings at risk (DEAR) = ($ Yalue of position) x (Price volatility) Dollar value of position = $400m./(1 + 0.095)15 = $ 102,529,300. Therefore, DEAR = $102,5293,500 x 0.03425 = $3,511,279. d. If the price volatility is based on a 90 percent confidence limit and a mean historical change in daily yields of 0.0 percent, what is the implied standard deviation of daily yield changes? d. If the price volatility is based on a 99 percent confidence limit and a mean historical change in daily yields of 0.0 percent, what is the implied standard deviation of daily yield changes? d. If the price volatility is based on 90 percent confidence limit and a mean historical change in daily yields of 0.0 percent, what is the implied standard deviation of daily yield changes? d. The potential adverse move in yields (PAMY)= confidence limit value x standard deviation value. Therefore, 25 basis points = 1.65 x o, and o=.0025/1.65 = .001515 or 15.15 basis points. Since the adverse move will be calculated on the basis of normal distribution with 99% confidence level. The probability factor from statistics is 2.33 as it will cover the 99% area and only 1% chances will be left for the adverse movement. be 1-5%= 0.95 check table close to 0.95=1.65 Potential adverse move in yield (PAMY) at 1 percent can be calculated as below: PAMY = 2.330 0.0025 = 2.33x 0.0025 2.33 = 0.001073or 10.73basis points o= 90% Thus, the standard deviation for these bonds is 10.73basis points 1-0.5% = 0.995 check table close to 0.995 is not equal 2.33