1. Swaps + Bonds

2. Swaps
Interest rates could change over time , investors may consider entering a swap To get constant rate (Swap rate) on their investments.

3. Swaps 𝑌𝑒𝑎𝑟 1 4% 𝑅 𝑌𝑒𝑎𝑟 2 5% 𝑌𝑒𝑎𝑟 3 6% Floating / Changing Rates
Constant / Swap
Rates
𝑌𝑒𝑎𝑟 1 4% 𝑅
𝑌𝑒𝑎𝑟 2 5%
𝑌𝑒𝑎𝑟 3 6%

4. PV of Interest payments PV of Interest payments
Swaps
PV of Interest payments
By changing rates
PV of Interest payments
By the Swap rate =

5. PV of Interest payments
Example
50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%.
𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒂𝒚𝒎𝒆𝒏𝒕𝒔:
𝒇 𝟎,𝟏 ∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟏
𝒇 𝟏,𝟐 ∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟐
𝒇 𝟐,𝟑 ∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟑
PV of Interest payments
By changing rates

6. PV of Interest payments
Example
50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%.
𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒂𝒚𝒎𝒆𝒏𝒕𝒔:
𝟎.𝟎𝟒∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 =𝟐,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟏
𝟎.𝟎𝟔𝟎𝟎𝟗𝟔𝟐∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎=𝟑,𝟎𝟎𝟒,𝟖𝟏𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟐
𝟎.𝟎𝟖𝟎𝟐𝟖𝟔𝟔∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎=𝟒,𝟎𝟏𝟒,𝟑𝟑𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟑
𝑃𝑉= 0.04∙50,000, ∙50,000, ∙50,000,
= 2,000, ,004, ,014,
PV of Interest payments
By changing rates

7. PV of Interest payments
Example
50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%.
𝑃𝑉= 0.04∙50,000, ∙50,000, ∙50,000,
𝑃𝑉=50,000,
PV of Interest payments
By changing rates

8. PV of Interest payments
Example
50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%.
𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒂𝒚𝒎𝒆𝒏𝒕𝒔:
𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟏
𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟐
𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟑
PV of Interest payments
By the Swap rate

9. PV of Interest payments
Example
50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%.
𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒂𝒚𝒎𝒆𝒏𝒕𝒔:
𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟏
𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟐
𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟑
𝑃𝑉= 𝑅∙50,000, 𝑅∙50,000, 𝑅∙50,000,
𝑃𝑉=50,000,000 𝑅 𝑅 𝑅
PV of Interest payments
By the Swap rate

10. Example 50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%.
50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%.
50,000, =50,000,000 𝑅 𝑅 𝑅
=𝑅∙ 𝑅=

11. Example (Faster Approach)
𝑊𝑒 𝑐𝑎𝑛 𝑤𝑜𝑟𝑘 𝑎𝑠 𝑤𝑒 ℎ𝑎𝑣𝑒 𝑎 𝑏𝑜𝑛𝑑 𝑤𝑖𝑡ℎ 𝐹=1 , 𝐶=1 ,𝑃=1 , 𝑟=𝑅
𝑃=𝐹𝑟∙ 𝑎 𝑛 +𝐶 𝑣 𝑛
1=1∙𝑅∙ ∙ 𝑅=

12. BONDS
Introduction
THERE ARE TWO WAYS FOR A CORPORATION TO RAISE CAPITAL
ISSUE DEPT
COMMENLY BONDS
ISSUE EQUITY
COMMENLY STOCKS

13. WHAT IS A BOND? A BOND IS A LOAN BORROWS FROM BOND ISSUER (BORROWER)
INVESTOR
(LENDER)

14. BONDS PAYS COUPONS REDEMPTION VALUE SYSTIMATIC INSTALLMENTS CALLED
A FINAL BALLOON PAYMENT CALLED
REDEMPTION VALUE

15. BONDS - TERMENOLOGY r – COUPON RATE PERCETAGE OF THE FACE AMOUNT
F – FACE AMOUNT COUPONS ARE CALCULATED BASED ON IT
C – REDEMPTION VALUE FINAL PAYMENT
Fr – COUPON AMOUNT (SYSTIMATIC PAYMENTS)
r – COUPON RATE PERCETAGE OF THE FACE AMOUNT

16. Example
To fund a project the government issues a block of bonds each has a coupon rate of 6% convertible semiannually for 5 years and pays 1000 at redemption where 𝒊 (𝟐) =𝟒%.
𝑭=𝑪=𝟏𝟎𝟎𝟎
𝒓= 𝟔% 𝟐 =𝟑%
𝑭𝒓=𝟑𝟎

17. BONDS ARE LOANS IN LOANS : IN BONDS :
𝑳𝑶𝑨𝑵 𝑨𝑴𝑶𝑼𝑵𝑻 = 𝑻𝑯𝑬 𝑷𝑹𝑺𝑬𝑺𝑬𝑵𝑻 𝑽𝑨𝑳𝑼𝑬 𝑶𝑭 𝑨𝑳𝑳 𝑷𝑨𝒀𝑴𝑬𝑵𝑻𝑺
IN BONDS :
𝑷𝑹𝑰𝑪𝑬 𝑶𝑭 𝑨 𝑩𝑶𝑵𝑫 = 𝑻𝑯𝑬 𝑷𝑹𝑺𝑬𝑺𝑬𝑵𝑻 𝑽𝑨𝑳𝑼𝑬 𝑶𝑭 𝑨𝑳𝑳 𝑷𝑨𝒀𝑴𝑬𝑵𝑻𝑺
=𝑷𝑹𝑬𝑺𝑬𝑵𝑻 𝑽𝑨𝑳𝑼𝑬 𝑶𝑭 𝑪𝑶𝑼𝑷𝑶𝑵𝑺 + 𝑷𝑹𝑺𝑬𝑺𝑬𝑵𝑻 𝑽𝑨𝑳𝑼𝑬 𝑶𝑭 𝑻𝑯𝑬 𝑹𝑬𝑫𝑬𝑴𝑷𝑻𝑰𝑶𝑵 𝑽𝑨𝑳𝑼𝑬

18. REMEMBER LOANS 𝐋=𝐀 𝑎 𝑛 𝑨𝑺𝑺𝑼𝑴𝑬 𝒏−𝒀𝑬𝑨𝑹 𝑳𝑶𝑨𝑵 𝑾𝑰𝑻𝑯 : 𝑨𝑵𝑵𝑼𝑨𝑳 𝑷𝑨𝒀𝑴𝑬𝑵𝑻𝑺 𝑶𝑭 𝑨
𝑨 𝑨 𝑨
𝑨 𝑨
… … …
n n
𝐋=𝐀 𝑎 𝑛

19. Back to BONDS C
Fr Fr Fr
Fr Fr
… … …
n n
𝑃=𝐹𝑟 𝑎 𝑛 +𝐶 𝑣 𝑛

20. Bonds Pricing - Example
To fund a project the government issues a block of bonds each has a coupon rate of 6% convertible semiannually for 5 years and pays 1000 at redemption where 𝒊 (𝟐) =𝟒%.
𝑭=𝑪=𝟏𝟎𝟎𝟎
𝒓= 𝟔% 𝟐 =𝟑%
𝑭𝒓=𝟑𝟎
𝑃=𝟑𝟎 𝑎 𝟏𝟎 𝟒% +𝟏𝟎𝟎𝟎 𝑣 𝟏𝟎