今天幫主邀請Yvonne老師來為大家接著講解CVP analysis的習題~
同學們大家好，今天老師帶大家一起來看看CVP analysis這個部分的真題應該怎麼做~
01
2018.3&6
The Alka Hotel is situated in a major city close to many theatres and restaurants.
The Alka Hotel has 25 double bedrooms and it charges guests$180 per room per night,regardless of single or double occupancy.The hotel’s variable cost is$60 per occupied room per night.
The Alka Hotel is open for 365 days a year and has a 70%budgeted occupancy rate.Fixed costs are budgeted at$600,000 a year and accrue evenly throughout the year.
During the first quarter(Q1)of the year the room occupancy rates are significantly below the levels expected at other times of the year with the Alka Hotel expecting to sell 900 occupied room nights during Q1.Options to improve profitability are being considered,including closing the hotel for the duration of Q1 or adopting one of two possible projects as follows:
Project 1-Theatre package
For Q1 only the Alka Hotel management would offer guests a『theatre package』.Couples who pay for two consecutive nights at a special rate of$67·50 per room night will also receive a pair of theatre tickets for a payment of$100.
The theatre tickets are very good value and are the result of long negotiation between the Alka Hotel management and the local theatre.The theatre tickets cost the Alka Hotel$95 a pair.The Alka Hotel’s fixed costs specific to this project(marketing and administration)are budgeted at$20,000.
The hotel’s management believes that the『theatre package』will have no effect on their usual Q1 customers,who are all business travellers and who have no interest in theatre tickets,but will still require their usual rooms.
Project 2-Restaurant
There is scope to extend the Alka Hotel and create enough space to operate a restaurant for the benefit of its guests.
The annual costs,revenues and volumes for the combined restaurant and hotel are illustrated in the following graph:
Note:The graph does not include the effect of the『theatre package』offer.
Required:
(a)Using the current annual budgeted figures,and ignoring the two proposed projects,calculate the breakeven number of occupied room nights and the margin of safety as a percentage.(4 marks)
(b)Ignoring the two proposed projects,calculate the budgeted profit or loss for Q1 and explain whether the hotel should close for the duration of Q1.(4 marks)
(c)Calculate the breakeven point in sales value of Project 1 and explain whether the hotel should adopt the project.(4 marks)
(d)Using the graph,quantify and comment upon the financial effect of Project 2 on the Alka Hotel.
Note:There are up to four marks available for calculations.(8 marks)
02
分析過程
第一步：首先看分數，按分估小點，宜多不宜減；
4分的題目通常就需要回答到兩個點，如果題中考的是簡單定義的默寫有可能會一分一個點；
8分的題目通常是4個點每個點2分。
第二步：問題要先讀，圈出關鍵詞，分析知識點；
(a)計算BEP和margin of safety as a percentage，結合上一步的分析，確定按照一個計算兩分寫；（需要注意的是，考生做題的時候過程儘量寫詳細，結果算錯了但是過程正確是有分的）
(b)忽略這兩個項目，計算第一季度的預算利潤或虧損，並解釋酒店是否應該在第一季度關閉。基本可以看出是calculate和explain一個兩分。
(c)計算項目1的BER，說明酒店是否應該採用該項目。基本可以看出是calculate和explain一個兩分。
(d)利用圖表，量化並評論項目2對Alka酒店的財務影響。下面批註了計算可以佔4分，剩下四分是文字。
以上是對問題的分析，可以看出前面兩個問題都是和project 1&2沒有關係的，所以先帶著前兩個問題看Project 1-Theatre package之前的背景。然後再分別看第三個和第四個問題。
第三步：開始讀題目，帶著問題讀，高亮標題幹；
(a)(b)問先讀Project 1-Theatre package之前：
25 double bedrooms，$180 per room per night：25間雙人房，無論是單人房還是雙人房，每個房間每晚收費180美元
variable cost is$60 per occupied room per night：每間客房每晚60美元
365 days a year,70%budgeted occupancy rate
Fixed costs$600,000 a year
First quarter(Q1)sell 900 occupied room nights
(a)問的是計算，先把公式寫上，然後帶入數據。帶數據過程中發現由某一個數據是題中沒有告訴的，建議寫Working，因為機考時EXCEL表格不能插入行。
BEP=Fixed cost/contribution per room per night=$600,000/$120(W1)=5000 occupied room nights
Margin of safety as a percentage=(Budgeted room occupancy–breakeven room occupancy)/budgeted room occupancy=(6387.5(w2)-5000)/6387.5(w2)=21.72%
Working 1:
Contribution per room=sales price per room per night-variable cost=$180-$60=$120 per room per night
Working 2:
Budgeted room occupancy=25 double bedrooms*365 days a year*70%budgeted occupancy rate=6387.5 occupied room nights
(b)問的是計算結合文字，習慣寫法是先把計算寫出來，然後再分析。
Profit or loss for Q1：
Total Contribution=Contribution per room*occupied room nights=$120*900=$108000
Profit/loss=total contribution-FC=$108000-$600,000*(3/12)=$-42000
（一定要注意這裡的FC只算一個季度的，也就是3個月）
Explain whether the hotel should close for the duration of Q1：
如果關閉，損失銷售收入節約變動成本，也就是損失contribution：108000
但是固定成本$600,000*(3/12)=150000不會被節約，普通的固定成本只有關閉企業完全不生產之後才可以被節約。
所以最後觀點是should not close，書寫過程為：
The Alka Hotel should not close in Q1.（先把觀點擺出來）
The fixed costs will still be incurred and closure would result in lost contribution of$108,000.This in turn would result in a decrease in annual profits of$108,000.（根據背景解釋原因）
In addition,the hotel could lose customers at other times of the year,particularly their regular business customers,who may perceive the hotel as being unreliable.（開腦洞，根據實際情況去分析有可能出現的情況，這一點不一定和答案相同，言之有理即可）
two consecutive nights at a special rate of$67.50 per room night will also receive a pair of theatre tickets for a payment of$100.：連續兩晚以67.50美元/間的特殊價格入住的夫婦還將獲得兩張劇院門票。也就是sales price=$67.50*2+$100=$235.
theatre tickets cost$95 a pair
fixed costs specific to this project$20,000.
(c)問的是計算結合文字，習慣寫法是先把計算寫出來，然後再分析。需要注意的是本小問的項目是一個單獨的項目，對原來的客戶沒有影響（have no effect on their usual Q1 customers），所以評估的時候也是單獨評估。
BER of project 1=Fixed cost/C/S ratio=$20,000/8.51%（w3）=$235017.63
Working 3：注意收入和變動成本都是由兩個部分組成。
Sales price=$67.50*2+$100=$235
VC=$60*2+$95=$215
Contribution=$235-$215=$20
C/S ratio=$40/$235.=8.51%
Explain whether the hotel should adopt the project:
從上面的計算可以看出，單位貢獻是$20比較低，如果要讓contribution覆蓋掉固定成本$20,000，需要1000個兩晚+影院票賣出去，也就是2000 occupied room nights。Q1可獲得的房間數是25*365*（3/12）=2281.25 room nights，其中正常的客戶需要900晚，所以是不夠的，should not adopt project 1.
Project 1 is not viable at the quoted prices.（通常習慣把結論放前面，讓考官明確你的觀點）
The unit contribution per theatre package is low and it requires a large number of sales to break even.Each theatre package would require two room nights to be sold which would mean 2,000 room nights needed in Q1 to break even.（需要的）
The available rooms for Q1 are only 2,281·25(9,125/4)and the Alka Hotel has already sold 900 rooms,so there is insufficient capacity.（可獲得的）
(這個題的題幹很少，主要是圖像，所以先在草稿紙上分析圖像）
(d)問是文字+計算，但是不按照先寫計算再寫文字，因為計算一開始沒辦法明確算的是什麼，最好是根據文字的邏輯去計算。
銷售收入：找到sales直線上唯一一個標了橫縱坐標的點(8000,2000000)，所以sales price=2000000/80000=$250，以前是$180 per room per night，可以看出餐廳業務平均每間房每晚增加了70的收入。
變動成本：total cost和fixed cost之間的差異就是VC，所以8000 rooms對應的VC是1560000-800000=760000，VC per room=760000/8000=$95 per room。相比於以前的$60 per room增加了$35 per room，這反映了餐廳業務的可變成本。
固定成本：從600000變到了800000，因為餐廳業務增加了200000的成本；
由於這些變化，收支平衡點從5000間客房增加到5161間客房（圖中直接看出），因此酒店需要銷售更多的客房夜來彌補成本。
當前的預計銷售房間數是7300（圖像中），佔總數的80%（7300/9125），安全邊際是（7300-5161）/7300=29.30%，這是大於當前的安全邊際的（29.30%>21.72%），風險更小了。
利潤：sales-total cost=7300*$250-7300*$95 per room-800000=$331,500
今天的內容就到這裡啦~