FF Qs & As Topic 3 Part 1 - FEEDBACKFORUM TOPIC3...

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FEEDBACK FORUM  TOPIC 3  VALUATION  PART 1 - BONDS Question 1 A debt security has four years to maturity, pays $1000 in annual interest and has a face value of  $10,000. The required rates of return are 4% for the first year, 6% for the second year, 3% for the  third year and 5% for the fourth year. What is the present value of the security?  a) $11,975.62  b)  $10,675  c)  $10,000  d)  $7,577  Timeline:                 CF 1                 CF 2                 CF 3                   CF 4            $1,000          $1,000           $1,000             $1,000             $10,000        4%               6%                3%                 5% 0                  1                  2                   3                     4 Treat each CF as a single sum because of the differing discount rates. Find PV of each CF using PV of a single sum formula = PV = FV(1+r) -n    Optimal Method (much quicker) To find PV of CF do the following: PV CFn  = CF n (1+r n ) -1  (1+r n-1 ) -1  (1+r n-2 ) -1  (1+r n-3 ) -1 ……. CF 4  =   $10,000 (face value) + $1,000 (coupon payment) = $11,000 (to be received at the end of  Period 4) CF 3  =   $1,000 (coupon payment to be received at the end of Period 3) CF 2  =   $1,000 (coupon payment to be received at the end of Period 2) CF 1  = $1,000 (coupon payment to be received at the end of Period 1) 1
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Step 1: PV of CF 4    PV CF4  = $11,000 (1+0.05) -1  (1+0.03) -1  (1+0.06) -1  (1+0.04) -1  =  $9,226.27 Step 2: PV of CF 3      PV CF3  = $1,000 (1+0.03) -1  (1+0.06) -1  (1+0.04) -1  =  $880.68 Step 3: PV of CF 2     PV CF2  = $1,000 (1+0.06) -1  (1+0.04) -1  =  $907.10 Step 4: PV of CF 1     PV CF1  = $1,000 (1+0.04) -1  =  $961.53 Step 5: Sum PVs $9,226.27       +   $   880.68            +   $   907.10       +   $   961.53          $11,975.58 Long Method  CF 4  = $10,000 (face value) + $1,000 (coupon payment) = $11,000 a. discount CF 4  back from T 4  to T 3  @ 5% PV 3  = $11,000(1+0.05) -1  = $10,476.19 b. discount PV 3  back from T 3  to T 2  @ 3% PV 2  = $10,476.19(1+0.03) -1  = $10,171.05 c. discount PV 2  back from T 2  to T 1  @ 6% PV 1  = $10,171.05(1+0.06) -1  = $9,595.33 d. discount PV 1  back from T 1  to T 0  @ 4% PV 0  = $9,595.33(1+0.04) -1  =  $9,226.27 Step 2: PV of CF 3      CF 3  = $1,000 (coupon payment) a. discount CF 3  back from T 3  to T 2 @3% PV 2  = $1,000(1+0.03) -1  = $970.87 b. discount PV 2  back from T 2  to T
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FF Qs & As Topic 3 Part 1 - FEEDBACKFORUM TOPIC3...

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