VIPSolutionsi need step by step solutionNew Buses Ventres nc hasan oustanding perpetal bond wih 12 percent coupon ate hat can be cold none year. The bond mokes nna! coupon paymerts, The cl remus sto 150 over pt sau. Thre 35 percent chance ht he Focal 0 Yea willbe 1 perce, anc G5 percent chance at the tres ote wh ptent Ip conc merase 15 peo, at Th utente yes marke pc ote Boe Oo und edn clcmton Roun heft snr 10:2 deci pcs. Ont in you espns: re SC)
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i need step by step solution
New Buses Ventres nc hasan oustanding perpetal bond wih 12 percent coupon ate hat can be cold none year. The bond
mokes nna! coupon paymerts, The cl remus sto 150 over pt sau. Thre 35 percent chance ht he Focal
0 Yea willbe 1 perce, anc G5 percent chance at the tres ote wh ptent Ip conc merase 15 peo,
at Th utente yes marke pc ote Boe
Oo und edn clcmton Roun heft snr 10:2 deci pcs. Ont in you espns:
re SC)
This is AI generated Response.
Asked by: Rohit Vaghela
Created at: 2026-01-26 01:16:04
Asked by: Rohit Vaghela
Created at: 2026-01-26 01:16:04
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Let's break down the problem step by step:
---
## **Step 1: Understand the Problem Data**
- **Coupon rate:** 12% (perpetual, so it pays $12 per year if par = $100)
- **Callable in one year, call premium:** $150 over par value (if par value = $100, call price = $250)
- **Probabilities for next year's interest rate:**
- 35% chance: interest rate = 14%
- 65% chance: interest rate = 9%
- **Current interest rate:** 12%
- **Current price of the bond?**
---
## **Step 2: Calculate Bond Value in Each Scenario**
### **If the bond is not called after 1 year:**
- If not called, the bond continues as a perpetual bond, so:
- Value = Coupon / Next year’s interest rate
### **If the bond is called after 1 year:**
- Holder receives the call price ($250) at the end of 1 year.
---
## **Step 3: Find the Value in Each Scenario in 1 Year**
### **Scenario 1: Interest rate goes to 14% (probability = .35)**
- The company will **not call** the bond (since $100/.14 = $85.71 < $250).
- Bond value = $12 / .14 = $85.71
### **Scenario 2: Interest rate goes to 9% (probability = .65)**
- The company will **call** the bond (since $12/.09 = $133.33 < $250, so bondholder gets $250).
---
## **Step 4: Calculate Expected Value Next Year**
\[
\text{Expected Value} = (Prob_1 \times Value_1) + (Prob_2 \times Value_2)
\]
\[
= (.35 \times 85.71) + (.65 \times 250)
\]
\[
= 30.00 + 162.50 = 192.50
\]
---
## **Step 5: Calculate the Current Price (Present Value)**
Discount the expected value and the coupon received this year back at the current interest rate (12%).
\[
\text{Current Price} = \frac{\text{Coupon}}{1.12} + \frac{\text{Expected Value}}{1.12}
\]
\[
= \frac{12}{1.12} + \frac{192.50}{1.12}
\]
\[
= 10.71 + 171.88 = 182.59
\]
---
## **Final Answer**
\[
\boxed{182.59}
\]
---
### **Summary Table**
| Scenario | Probability | Value in 1 Yr | Weighted Value |
|-----------------|-------------|---------------|---------------|
| Rate = 14% | .35 | $85.71 | $30.00 |
| Rate = 9% | .65 | $250.00 | $162.50 |
| **Expected Value** | | | **$192.50** |
---
**The current one-year market price of the bond is $182.59** (rounded to 2 decimals, omit $ sign in the answer box: `182.59`).
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