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MArishka [77]
3 years ago
10

Chris purchased a 10 year 100 par value bond where 6% coupons are paid semiannually. Cheryl purchased a 100 par value bond where

6% coupons are paid semiannually. There is no maturity date or redemption value for Cheryl’s bond. Cheryl paid $100 for her bond. The yield for Chris’s bond is 80% of the yield for Cheryl’s bond. How much did Chris pay for his bond?
Business
1 answer:
WITCHER [35]3 years ago
8 0

Answer:

Chris paid $109.68 for his bond. Since he paid a premium for the bond, the YTM is lower than the coupon rate.

Explanation:

yield of Cheryl's bond is 6% since she purchased it at par and the bond's coupon is 6%

if Chris's bond yields 80% of Cheryl's, it will yield 6% x 0.8 = 4.8%

we can use the approximate yield to maturity formula to find the market price of Chris's bond:

2.4%(semiannual) = {3 + [(100 - MV)/20]} / [(100 + MV)/2]

0.024 x [(100 + MV)/2] = 3 + [(100 - MV)/20]

0.024 x (50 + 0.5MV) = 3 + 5 - 0.05MV

1.2 + 0.012MV = 8 - 0.05MV

0.062MV = 6.8

MV = 6.8 / 0.062 = 109.68

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8 0
3 years ago
Maggie Stewart loves desserts. But, due to weight and cholesterol concerns, she has decided that she must plan her desserts care
nika2105 [10]

Answer:

The option that maximizes Maggie's taste index is 1 snack bar and 2 ice creams

Explanation:

<u>snack bar</u>                  <u>ice cream</u>

37 grams                   65 grams

120 calories              160 calories

5 grams of fat           10 grams of fat

Maggie wants to consume up to 450 calories and 25 grams of fat, but she needs at least 120 grams of dessert per day. Ice cream taste 95, snack bars 85.

  • maximize taste index = [85(37X) + 95(65Y)] / (37X + 65Y)
  • 5X + 10Y ≤ 25 ⇒ CONSTRAINT 1
  • 120X + 160Y ≤ 450 ⇒ CONSTRAINT 2
  • 37X + 65Y ≥ 120 ⇒ CONSTRAINT 3
  • X ≥ 0 ⇒ CONSTRAINT 4
  • Y ≥ 0 ⇒ CONSTRAINT 5

maximum possible combinations following constraint 1, 4 AND 5:

  • option 1: 1 snack bar - 2 ice creams (5 + 20 = 25)
  • option 2: 2 snack bars - 1 ice cream (10 + 10 = 20)
  • option 3: 3 snack bars - 1 ice cream (15 + 10 = 25)

possible combinations following constraint 2:

  • option 1: 1 snack bar - 2 ice creams (120 + 320 = 440)
  • option 2: 2 snack bars - 1 ice cream (240 + 160 = 400)

possible combination following constraint 3:

  • option 1: 1 snack bar - 2 ice creams (37 + 130 = 167)
  • option 2: 2 snack bars - 1 ice cream (74 + 65 = 139)

since we only have two possibilities, we can calculate which one generates the highest taste index

maximize taste index = [85(37X) + 95(65Y)] / (37X + 65Y)

  • option 1: 1 snack bar - 2 ice creams = [85(37) + 95(130)] / (37 + 130) = (3,145 + 12,350) / 167 = 92.78
  • option 2: 2 snack bars - 1 ice cream = [85(74) + 95(65)] / (74 + 65) = (6,290 + 6,175) / 139 = 89.68

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